LMFDB - Embedded newform 13.5.d.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,5,Mod(5,13)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34380952009$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.53039932416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 12x^{3} + 529x^{2} - 1334x + 1682 $ x^6 - 2x^5 + 2x^4 - 12x^3 + 529x^2 - 1334*x + 1682
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.2
Root			$1.30633 - 1.30633i$ of defining polynomial
Character	$\chi$	$=$	13.5
Dual form			13.5.d.a.8.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30633 + 1.30633i) q^{2} +9.97438 q^{3} +12.5870i q^{4} +(9.28070 - 9.28070i) q^{5} +(-13.0298 + 13.0298i) q^{6} +(-46.1782 - 46.1782i) q^{7} +(-37.3440 - 37.3440i) q^{8} +18.4882 q^{9} +O(q^{10})$	\(q+(-1.30633 + 1.30633i) q^{2} +9.97438 q^{3} +12.5870i q^{4} +(9.28070 - 9.28070i) q^{5} +(-13.0298 + 13.0298i) q^{6} +(-46.1782 - 46.1782i) q^{7} +(-37.3440 - 37.3440i) q^{8} +18.4882 q^{9} +24.2472i q^{10} +(90.5598 + 90.5598i) q^{11} +125.548i q^{12} +(-37.9467 - 164.685i) q^{13} +120.648 q^{14} +(92.5693 - 92.5693i) q^{15} -103.826 q^{16} +298.690i q^{17} +(-24.1516 + 24.1516i) q^{18} +(145.723 - 145.723i) q^{19} +(116.816 + 116.816i) q^{20} +(-460.599 - 460.599i) q^{21} -236.601 q^{22} +72.2918i q^{23} +(-372.483 - 372.483i) q^{24} +452.737i q^{25} +(264.702 + 165.561i) q^{26} -623.516 q^{27} +(581.247 - 581.247i) q^{28} +1458.98 q^{29} +241.851i q^{30} +(-974.947 + 974.947i) q^{31} +(733.134 - 733.134i) q^{32} +(903.278 + 903.278i) q^{33} +(-390.187 - 390.187i) q^{34} -857.133 q^{35} +232.712i q^{36} +(345.648 + 345.648i) q^{37} +380.723i q^{38} +(-378.495 - 1642.63i) q^{39} -693.156 q^{40} +(-546.990 + 546.990i) q^{41} +1203.38 q^{42} -2284.35i q^{43} +(-1139.88 + 1139.88i) q^{44} +(171.584 - 171.584i) q^{45} +(-94.4365 - 94.4365i) q^{46} +(-1932.68 - 1932.68i) q^{47} -1035.60 q^{48} +1863.86i q^{49} +(-591.422 - 591.422i) q^{50} +2979.25i q^{51} +(2072.89 - 477.636i) q^{52} +4356.45 q^{53} +(814.515 - 814.515i) q^{54} +1680.92 q^{55} +3448.95i q^{56} +(1453.50 - 1453.50i) q^{57} +(-1905.90 + 1905.90i) q^{58} +(-1548.85 - 1548.85i) q^{59} +(1165.17 + 1165.17i) q^{60} -897.748 q^{61} -2547.20i q^{62} +(-853.754 - 853.754i) q^{63} +254.209i q^{64} +(-1880.56 - 1176.22i) q^{65} -2359.95 q^{66} +(2232.99 - 2232.99i) q^{67} -3759.63 q^{68} +721.065i q^{69} +(1119.69 - 1119.69i) q^{70} +(-1218.01 + 1218.01i) q^{71} +(-690.424 - 690.424i) q^{72} +(1615.47 + 1615.47i) q^{73} -903.058 q^{74} +4515.77i q^{75} +(1834.22 + 1834.22i) q^{76} -8363.78i q^{77} +(2640.24 + 1651.37i) q^{78} -1235.04 q^{79} +(-963.576 + 963.576i) q^{80} -7716.73 q^{81} -1429.09i q^{82} +(-2620.61 + 2620.61i) q^{83} +(5797.57 - 5797.57i) q^{84} +(2772.06 + 2772.06i) q^{85} +(2984.10 + 2984.10i) q^{86} +14552.4 q^{87} -6763.72i q^{88} +(2845.64 + 2845.64i) q^{89} +448.288i q^{90} +(-5852.54 + 9357.16i) q^{91} -909.938 q^{92} +(-9724.49 + 9724.49i) q^{93} +5049.40 q^{94} -2704.82i q^{95} +(7312.55 - 7312.55i) q^{96} +(-4189.00 + 4189.00i) q^{97} +(-2434.80 - 2434.80i) q^{98} +(1674.29 + 1674.29i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9} - 32 q^{11} - 244 q^{14} + 404 q^{15} + 1044 q^{16} - 802 q^{18} + 732 q^{19} + 428 q^{20} - 2128 q^{21} - 1632 q^{22} - 24 q^{24} + 910 q^{26} + 236 q^{27} + 1884 q^{28} + 4184 q^{29} - 3468 q^{31} + 2092 q^{32} + 2324 q^{33} - 5304 q^{34} - 4204 q^{35} - 1758 q^{37} + 1196 q^{39} - 708 q^{40} + 4750 q^{41} + 9532 q^{42} - 3956 q^{44} + 830 q^{45} + 516 q^{46} - 6872 q^{47} - 9436 q^{48} - 322 q^{50} + 3900 q^{52} + 2108 q^{53} - 184 q^{54} + 6408 q^{55} - 5800 q^{57} + 6516 q^{58} + 4372 q^{59} + 1324 q^{60} + 5988 q^{61} - 652 q^{63} - 5018 q^{65} - 4592 q^{66} + 72 q^{67} - 10572 q^{68} + 7368 q^{70} - 14672 q^{71} - 7980 q^{72} + 5874 q^{73} + 1544 q^{74} + 3576 q^{76} + 5720 q^{78} + 2616 q^{79} - 12080 q^{80} - 19450 q^{81} + 19264 q^{83} + 6296 q^{84} + 4164 q^{85} + 29376 q^{86} + 35584 q^{87} - 986 q^{89} - 30888 q^{91} + 5304 q^{92} - 9520 q^{93} - 36156 q^{94} + 20720 q^{96} - 23154 q^{97} - 41426 q^{98} + 17492 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9 - 32 * q^11 - 244 * q^14 + 404 * q^15 + 1044 * q^16 - 802 * q^18 + 732 * q^19 + 428 * q^20 - 2128 * q^21 - 1632 * q^22 - 24 * q^24 + 910 * q^26 + 236 * q^27 + 1884 * q^28 + 4184 * q^29 - 3468 * q^31 + 2092 * q^32 + 2324 * q^33 - 5304 * q^34 - 4204 * q^35 - 1758 * q^37 + 1196 * q^39 - 708 * q^40 + 4750 * q^41 + 9532 * q^42 - 3956 * q^44 + 830 * q^45 + 516 * q^46 - 6872 * q^47 - 9436 * q^48 - 322 * q^50 + 3900 * q^52 + 2108 * q^53 - 184 * q^54 + 6408 * q^55 - 5800 * q^57 + 6516 * q^58 + 4372 * q^59 + 1324 * q^60 + 5988 * q^61 - 652 * q^63 - 5018 * q^65 - 4592 * q^66 + 72 * q^67 - 10572 * q^68 + 7368 * q^70 - 14672 * q^71 - 7980 * q^72 + 5874 * q^73 + 1544 * q^74 + 3576 * q^76 + 5720 * q^78 + 2616 * q^79 - 12080 * q^80 - 19450 * q^81 + 19264 * q^83 + 6296 * q^84 + 4164 * q^85 + 29376 * q^86 + 35584 * q^87 - 986 * q^89 - 30888 * q^91 + 5304 * q^92 - 9520 * q^93 - 36156 * q^94 + 20720 * q^96 - 23154 * q^97 - 41426 * q^98 + 17492 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.30633	+	1.30633i	−0.326581	+	0.326581i	−0.851285	−	0.524704i	$-0.824176\pi$
$2$	−1.30633	+	1.30633i	−0.326581	+	0.326581i	0.524704	+	0.851285i	$0.324176\pi$
$3$	9.97438			1.10826			0.554132	−	0.832429i	$-0.313050\pi$
$3$	9.97438			1.10826			0.554132	+	0.832429i	$0.313050\pi$
$4$			12.5870i			0.786689i
$5$	9.28070	−	9.28070i	0.371228	−	0.371228i	−0.496696	−	0.867924i	$-0.665454\pi$
$5$	9.28070	−	9.28070i	0.371228	−	0.371228i	0.867924	+	0.496696i	$0.165454\pi$
$6$	−13.0298	+	13.0298i	−0.361938	+	0.361938i
$7$	−46.1782	−	46.1782i	−0.942413	−	0.942413i	0.0560172	−	0.998430i	$-0.482160\pi$
$7$	−46.1782	−	46.1782i	−0.942413	−	0.942413i	−0.998430	+	0.0560172i	$0.982160\pi$
$8$	−37.3440	−	37.3440i	−0.583499	−	0.583499i
$9$	18.4882			0.228250
$10$			24.2472i			0.242472i
$11$	90.5598	+	90.5598i	0.748428	+	0.748428i	0.974184	−	0.225756i	$-0.0724851\pi$
$11$	90.5598	+	90.5598i	0.748428	+	0.748428i	−0.225756	+	0.974184i	$0.572485\pi$
$12$			125.548i			0.871860i
$13$	−37.9467	−	164.685i	−0.224537	−	0.974466i
$13$	−37.9467	−	164.685i	−0.224537	−	0.974466i
$14$	120.648			0.615549
$15$	92.5693	−	92.5693i	0.411419	−	0.411419i
$16$	−103.826			−0.405569
$17$			298.690i			1.03353i	0.856127	+	0.516766i	$0.172864\pi$
$17$			298.690i			1.03353i	−0.856127	+	0.516766i	$0.827136\pi$
$18$	−24.1516	+	24.1516i	−0.0745421	+	0.0745421i
$19$	145.723	−	145.723i	0.403665	−	0.403665i	−0.475858	−	0.879522i	$-0.657862\pi$
$19$	145.723	−	145.723i	0.403665	−	0.403665i	0.879522	+	0.475858i	$0.157862\pi$
$20$	116.816	+	116.816i	0.292041	+	0.292041i
$21$	−460.599	−	460.599i	−1.04444	−	1.04444i
$22$	−236.601			−0.488845
$23$			72.2918i			0.136657i	0.997663	+	0.0683287i	$0.0217667\pi$
$23$			72.2918i			0.136657i	−0.997663	+	0.0683287i	$0.978233\pi$
$24$	−372.483	−	372.483i	−0.646671	−	0.646671i
$25$			452.737i			0.724379i
$26$	264.702	+	165.561i	0.391572	+	0.244913i
$27$	−623.516			−0.855303
$28$	581.247	−	581.247i	0.741386	−	0.741386i
$29$	1458.98			1.73481			0.867407	−	0.497600i	$-0.165785\pi$
$29$	1458.98			1.73481			0.867407	+	0.497600i	$0.165785\pi$
$30$			241.851i			0.268723i
$31$	−974.947	+	974.947i	−1.01451	+	1.01451i	−0.0146199	+	0.999893i	$0.504654\pi$
$31$	−974.947	+	974.947i	−1.01451	+	1.01451i	−0.999893	+	0.0146199i	$0.995346\pi$
$32$	733.134	−	733.134i	0.715951	−	0.715951i
$33$	903.278	+	903.278i	0.829456	+	0.829456i
$34$	−390.187	−	390.187i	−0.337532	−	0.337532i
$35$	−857.133			−0.699700
$36$			232.712i			0.179562i
$37$	345.648	+	345.648i	0.252482	+	0.252482i	0.821988	−	0.569505i	$-0.192865\pi$
$37$	345.648	+	345.648i	0.252482	+	0.252482i	−0.569505	+	0.821988i	$0.692865\pi$
$38$			380.723i			0.263659i
$39$	−378.495	−	1642.63i	−0.248846	−	1.07997i
$40$	−693.156			−0.433223
$41$	−546.990	+	546.990i	−0.325396	+	0.325396i	−0.850833	−	0.525437i	$-0.823902\pi$
$41$	−546.990	+	546.990i	−0.325396	+	0.325396i	0.525437	+	0.850833i	$0.323902\pi$
$42$	1203.38			0.682191
$43$		−	2284.35i		−	1.23545i	−0.786393	−	0.617726i	$-0.788054\pi$
$43$		−	2284.35i		−	1.23545i	0.786393	−	0.617726i	$-0.211946\pi$
$44$	−1139.88	+	1139.88i	−0.588780	+	0.588780i
$45$	171.584	−	171.584i	0.0847327	−	0.0847327i
$46$	−94.4365	−	94.4365i	−0.0446297	−	0.0446297i
$47$	−1932.68	−	1932.68i	−0.874910	−	0.874910i	0.118093	−	0.993003i	$-0.462322\pi$
$47$	−1932.68	−	1932.68i	−0.874910	−	0.874910i	−0.993003	+	0.118093i	$0.962322\pi$
$48$	−1035.60			−0.449478
$49$			1863.86i			0.776283i
$50$	−591.422	−	591.422i	−0.236569	−	0.236569i
$51$			2979.25i			1.14543i
$52$	2072.89	−	477.636i	0.766602	−	0.176641i
$53$	4356.45			1.55089			0.775445	−	0.631415i	$-0.217526\pi$
$53$	4356.45			1.55089			0.775445	+	0.631415i	$0.217526\pi$
$54$	814.515	−	814.515i	0.279326	−	0.279326i
$55$	1680.92			0.555675
$56$			3448.95i			1.09979i
$57$	1453.50	−	1453.50i	0.447367	−	0.447367i
$58$	−1905.90	+	1905.90i	−0.566558	+	0.566558i
$59$	−1548.85	−	1548.85i	−0.444945	−	0.444945i	0.448725	−	0.893670i	$-0.351878\pi$
$59$	−1548.85	−	1548.85i	−0.444945	−	0.444945i	−0.893670	+	0.448725i	$0.851878\pi$
$60$	1165.17	+	1165.17i	0.323659	+	0.323659i
$61$	−897.748			−0.241265			−0.120633	−	0.992697i	$-0.538492\pi$
$61$	−897.748			−0.241265			−0.120633	+	0.992697i	$0.538492\pi$
$62$		−	2547.20i		−	0.662642i
$63$	−853.754	−	853.754i	−0.215105	−	0.215105i
$64$			254.209i			0.0620628i
$65$	−1880.56	−	1176.22i	−0.445103	−	0.278395i
$66$	−2359.95			−0.541770
$67$	2232.99	−	2232.99i	0.497435	−	0.497435i	−0.413204	−	0.910639i	$-0.635590\pi$
$67$	2232.99	−	2232.99i	0.497435	−	0.497435i	0.910639	+	0.413204i	$0.135590\pi$
$68$	−3759.63			−0.813068
$69$			721.065i			0.151453i
$70$	1119.69	−	1119.69i	0.228509	−	0.228509i
$71$	−1218.01	+	1218.01i	−0.241620	+	0.241620i	−0.817520	−	0.575900i	$-0.804652\pi$
$71$	−1218.01	+	1218.01i	−0.241620	+	0.241620i	0.575900	+	0.817520i	$0.304652\pi$
$72$	−690.424	−	690.424i	−0.133184	−	0.133184i
$73$	1615.47	+	1615.47i	0.303147	+	0.303147i	0.842244	−	0.539097i	$-0.181234\pi$
$73$	1615.47	+	1615.47i	0.303147	+	0.303147i	−0.539097	+	0.842244i	$0.681234\pi$
$74$	−903.058			−0.164912
$75$			4515.77i			0.802804i
$76$	1834.22	+	1834.22i	0.317559	+	0.317559i
$77$		−	8363.78i		−	1.41066i
$78$	2640.24	+	1651.37i	0.433965	+	0.271428i
$79$	−1235.04			−0.197891			−0.0989455	−	0.995093i	$-0.531547\pi$
$79$	−1235.04			−0.197891			−0.0989455	+	0.995093i	$0.531547\pi$
$80$	−963.576	+	963.576i	−0.150559	+	0.150559i
$81$	−7716.73			−1.17615
$82$		−	1429.09i		−	0.212536i
$83$	−2620.61	+	2620.61i	−0.380406	+	0.380406i	−0.871248	−	0.490843i	$-0.836689\pi$
$83$	−2620.61	+	2620.61i	−0.380406	+	0.380406i	0.490843	+	0.871248i	$0.336689\pi$
$84$	5797.57	−	5797.57i	0.821652	−	0.821652i
$85$	2772.06	+	2772.06i	0.383676	+	0.383676i
$86$	2984.10	+	2984.10i	0.403475	+	0.403475i
$87$	14552.4			1.92263
$88$		−	6763.72i		−	0.873415i
$89$	2845.64	+	2845.64i	0.359253	+	0.359253i	0.863538	−	0.504285i	$-0.168244\pi$
$89$	2845.64	+	2845.64i	0.359253	+	0.359253i	−0.504285	+	0.863538i	$0.668244\pi$
$90$			448.288i			0.0553443i
$91$	−5852.54	+	9357.16i	−0.706743	+	1.12995i
$92$	−909.938			−0.107507
$93$	−9724.49	+	9724.49i	−1.12435	+	1.12435i
$94$	5049.40			0.571458
$95$		−	2704.82i		−	0.299703i
$96$	7312.55	−	7312.55i	0.793463	−	0.793463i
$97$	−4189.00	+	4189.00i	−0.445212	+	0.445212i	−0.893759	−	0.448547i	$-0.851942\pi$
$97$	−4189.00	+	4189.00i	−0.445212	+	0.445212i	0.448547	+	0.893759i	$0.351942\pi$
$98$	−2434.80	−	2434.80i	−0.253520	−	0.253520i
$99$	1674.29	+	1674.29i	0.170829	+	0.170829i
$100$	−5698.61			−0.569861
$101$		−	10674.4i		−	1.04641i	−0.852206	−	0.523206i	$-0.824736\pi$
$101$		−	10674.4i		−	1.04641i	0.852206	−	0.523206i	$-0.175264\pi$
$102$	−3891.87	−	3891.87i	−0.374075	−	0.374075i
$103$		−	13211.9i		−	1.24535i	−0.782482	−	0.622673i	$-0.786047\pi$
$103$		−	13211.9i		−	1.24535i	0.782482	−	0.622673i	$-0.213953\pi$
$104$	−4732.90	+	7567.06i	−0.437583	+	0.699617i
$105$	−8549.37			−0.775453
$106$	−5690.94	+	5690.94i	−0.506492	+	0.506492i
$107$	−5048.88			−0.440988			−0.220494	−	0.975388i	$-0.570767\pi$
$107$	−5048.88			−0.440988			−0.220494	+	0.975388i	$0.570767\pi$
$108$		−	7848.21i		−	0.672858i
$109$	6220.78	−	6220.78i	0.523591	−	0.523591i	−0.395063	−	0.918654i	$-0.629277\pi$
$109$	6220.78	−	6220.78i	0.523591	−	0.523591i	0.918654	+	0.395063i	$0.129277\pi$
$110$	−2195.82	+	2195.82i	−0.181473	+	0.181473i
$111$	3447.63	+	3447.63i	0.279817	+	0.279817i
$112$	4794.49	+	4794.49i	0.382214	+	0.382214i
$113$	11006.7			0.861984			0.430992	−	0.902356i	$-0.358164\pi$
$113$	11006.7			0.861984			0.430992	+	0.902356i	$0.358164\pi$
$114$			3797.48i			0.292204i
$115$	670.918	+	670.918i	0.0507311	+	0.0507311i
$116$			18364.2i			1.36476i
$117$	−701.567	−	3044.73i	−0.0512504	−	0.222422i
$118$	4046.62			0.290622
$119$	13793.0	−	13793.0i	0.974013	−	0.974013i
$120$	−6913.80			−0.480125
$121$			1761.16i			0.120289i
$122$	1172.75	−	1172.75i	0.0787927	−	0.0787927i
$123$	−5455.89	+	5455.89i	−0.360625	+	0.360625i
$124$	−12271.7	−	12271.7i	−0.798107	−	0.798107i
$125$	10002.2	+	10002.2i	0.640138	+	0.640138i
$126$	2230.56			0.140499
$127$			16682.3i			1.03431i	0.855893	+	0.517153i	$0.173008\pi$
$127$			16682.3i			1.03431i	−0.855893	+	0.517153i	$0.826992\pi$
$128$	11398.1	+	11398.1i	0.695682	+	0.695682i
$129$		−	22785.0i		−	1.36921i
$130$	3993.15	−	920.102i	0.236281	−	0.0544439i
$131$	21766.7			1.26838			0.634190	−	0.773177i	$-0.281334\pi$
$131$	21766.7			1.26838			0.634190	+	0.773177i	$0.281334\pi$
$132$	−11369.6	+	11369.6i	−0.652524	+	0.652524i
$133$	−13458.5			−0.760838
$134$			5834.01i			0.324906i
$135$	−5786.67	+	5786.67i	−0.317513	+	0.317513i
$136$	11154.3	−	11154.3i	0.603065	−	0.603065i
$137$	833.609	+	833.609i	0.0444142	+	0.0444142i	0.728965	−	0.684551i	$-0.240002\pi$
$137$	833.609	+	833.609i	0.0444142	+	0.0444142i	−0.684551	+	0.728965i	$0.740002\pi$
$138$	−941.946	−	941.946i	−0.0494616	−	0.0494616i
$139$	−21688.2			−1.12252			−0.561261	−	0.827639i	$-0.689683\pi$
$139$	−21688.2			−1.12252			−0.561261	+	0.827639i	$0.689683\pi$
$140$		−	10788.8i		−	0.550447i
$141$	−19277.2	−	19277.2i	−0.969631	−	0.969631i
$142$		−	3182.23i		−	0.157817i
$143$	11477.4	−	18350.3i	0.561268	−	0.897367i
$144$	−1919.55			−0.0925711
$145$	13540.3	−	13540.3i	0.644012	−	0.644012i
$146$	−4220.66			−0.198004
$147$			18590.8i			0.860327i
$148$	−4350.69	+	4350.69i	−0.198625	+	0.198625i
$149$	−28179.1	+	28179.1i	−1.26927	+	1.26927i	−0.322807	+	0.946465i	$0.604627\pi$
$149$	−28179.1	+	28179.1i	−1.26927	+	1.26927i	−0.946465	+	0.322807i	$0.895373\pi$
$150$	−5899.07	−	5899.07i	−0.262181	−	0.262181i
$151$	−15225.9	−	15225.9i	−0.667773	−	0.667773i	0.289427	−	0.957200i	$-0.406535\pi$
$151$	−15225.9	−	15225.9i	−0.667773	−	0.667773i	−0.957200	+	0.289427i	$0.906535\pi$
$152$	−10883.7			−0.471076
$153$			5522.26i			0.235903i
$154$	10925.8	+	10925.8i	0.460694	+	0.460694i
$155$			18096.4i			0.753232i
$156$	20675.8	−	4764.12i	0.849597	−	0.195764i
$157$	−5638.66			−0.228758			−0.114379	−	0.993437i	$-0.536488\pi$
$157$	−5638.66			−0.228758			−0.114379	+	0.993437i	$0.536488\pi$
$158$	1613.36	−	1613.36i	0.0646275	−	0.0646275i
$159$	43452.9			1.71880
$160$		−	13608.0i		−	0.531562i
$161$	3338.30	−	3338.30i	0.128788	−	0.128788i
$162$	10080.6	−	10080.6i	0.384109	−	0.384109i
$163$	22791.6	+	22791.6i	0.857826	+	0.857826i	0.991082	−	0.133255i	$-0.0425431\pi$
$163$	22791.6	+	22791.6i	0.857826	+	0.857826i	−0.133255	+	0.991082i	$0.542543\pi$
$164$	−6884.98	−	6884.98i	−0.255985	−	0.255985i
$165$	16766.1			0.615835
$166$		−	6846.75i		−	0.248467i
$167$	−11597.7	−	11597.7i	−0.415852	−	0.415852i	0.467919	−	0.883771i	$-0.345004\pi$
$167$	−11597.7	−	11597.7i	−0.415852	−	0.415852i	−0.883771	+	0.467919i	$0.845004\pi$
$168$			34401.2i			1.21886i
$169$	−25681.1	+	12498.5i	−0.899167	+	0.437606i
$170$	−7242.42			−0.250603
$171$	2694.16	−	2694.16i	0.0921364	−	0.0921364i
$172$	28753.2			0.971917
$173$		−	7266.07i		−	0.242777i	−0.992605	−	0.121388i	$-0.961265\pi$
$173$		−	7266.07i		−	0.242777i	0.992605	−	0.121388i	$-0.0387347\pi$
$174$	−19010.2	+	19010.2i	−0.627896	+	0.627896i
$175$	20906.6	−	20906.6i	0.682664	−	0.682664i
$176$	−9402.44	−	9402.44i	−0.303540	−	0.303540i
$177$	−15448.9	−	15448.9i	−0.493117	−	0.493117i
$178$	−7434.67			−0.234651
$179$			18706.0i			0.583816i	0.956446	+	0.291908i	$0.0942900\pi$
$179$			18706.0i			0.583816i	−0.956446	+	0.291908i	$0.905710\pi$
$180$	2159.73	+	2159.73i	0.0666583	+	0.0666583i
$181$			14931.3i			0.455765i	0.973689	+	0.227882i	$0.0731802\pi$
$181$			14931.3i			0.455765i	−0.973689	+	0.227882i	$0.926820\pi$
$182$	−4578.17	−	19868.8i	−0.138213	−	0.599831i
$183$	−8954.48			−0.267386
$184$	2699.66	−	2699.66i	0.0797395	−	0.0797395i
$185$	6415.72			0.187457
$186$		−	25406.7i		−	0.734382i
$187$	−27049.4	+	27049.4i	−0.773524	+	0.773524i
$188$	24326.6	−	24326.6i	0.688282	−	0.688282i
$189$	28792.9	+	28792.9i	0.806049	+	0.806049i
$190$	3533.38	+	3533.38i	0.0978775	+	0.0978775i
$191$	−34297.6			−0.940150			−0.470075	−	0.882626i	$-0.655773\pi$
$191$	−34297.6			−0.940150			−0.470075	+	0.882626i	$0.655773\pi$
$192$			2535.58i			0.0687820i
$193$	−5043.50	−	5043.50i	−0.135400	−	0.135400i	0.636159	−	0.771558i	$-0.280522\pi$
$193$	−5043.50	−	5043.50i	−0.135400	−	0.135400i	−0.771558	+	0.636159i	$0.780522\pi$
$194$		−	10944.4i		−	0.290796i
$195$	−18757.4	−	11732.0i	−0.493292	−	0.308535i
$196$	−23460.4			−0.610694
$197$	−9293.04	+	9293.04i	−0.239456	+	0.239456i	−0.816625	−	0.577169i	$-0.804157\pi$
$197$	−9293.04	+	9293.04i	−0.239456	+	0.239456i	0.577169	+	0.816625i	$0.304157\pi$
$198$	−4374.34			−0.111579
$199$			9337.31i			0.235785i	0.993026	+	0.117892i	$0.0376138\pi$
$199$			9337.31i			0.235785i	−0.993026	+	0.117892i	$0.962386\pi$
$200$	16907.0	−	16907.0i	0.422675	−	0.422675i
$201$	22272.7	−	22272.7i	0.551290	−	0.551290i
$202$	13944.3	+	13944.3i	0.341739	+	0.341739i
$203$	−67373.0	−	67373.0i	−1.63491	−	1.63491i
$204$	−37499.9			−0.901094
$205$			10152.9i			0.241592i
$206$	17259.0	+	17259.0i	0.406707	+	0.406707i
$207$			1336.55i			0.0311920i
$208$	3939.84	+	17098.5i	0.0910652	+	0.395213i
$209$	26393.3			0.604228
$210$	11168.3	−	11168.3i	0.253248	−	0.253248i
$211$	53816.1			1.20878			0.604390	−	0.796689i	$-0.293417\pi$
$211$	53816.1			1.20878			0.604390	+	0.796689i	$0.293417\pi$
$212$			54834.8i			1.22007i
$213$	−12148.9	+	12148.9i	−0.267779	+	0.267779i
$214$	6595.47	−	6595.47i	0.144019	−	0.144019i
$215$	−21200.4	−	21200.4i	−0.458635	−	0.458635i
$216$	23284.6	+	23284.6i	0.499069	+	0.499069i
$217$	90042.6			1.91218
$218$			16252.7i			0.341990i
$219$	16113.3	+	16113.3i	0.335967	+	0.335967i
$220$			21157.8i			0.437144i
$221$	49189.8	−	11334.3i	1.00714	−	0.232066i
$222$	−9007.44			−0.182766
$223$	27165.3	−	27165.3i	0.546266	−	0.546266i	−0.379093	−	0.925359i	$-0.623764\pi$
$223$	27165.3	−	27165.3i	0.546266	−	0.546266i	0.925359	+	0.379093i	$0.123764\pi$
$224$	−67709.6			−1.34944
$225$			8370.31i			0.165339i
$226$	−14378.3	+	14378.3i	−0.281508	+	0.281508i
$227$	−63491.1	+	63491.1i	−1.23214	+	1.23214i	−0.269003	+	0.963139i	$0.586694\pi$
$227$	−63491.1	+	63491.1i	−1.23214	+	1.23214i	−0.963139	+	0.269003i	$0.913306\pi$
$228$	18295.2	+	18295.2i	0.351939	+	0.351939i
$229$	21248.1	+	21248.1i	0.405180	+	0.405180i	0.880054	−	0.474874i	$-0.157506\pi$
$229$	21248.1	+	21248.1i	0.405180	+	0.405180i	−0.474874	+	0.880054i	$0.657506\pi$
$230$	−1752.88			−0.0331356
$231$		−	83423.5i		−	1.56338i
$232$	−54484.0	−	54484.0i	−1.01226	−	1.01226i
$233$		−	7414.27i		−	0.136570i	−0.997666	−	0.0682852i	$-0.978247\pi$
$233$		−	7414.27i		−	0.136570i	0.997666	−	0.0682852i	$-0.0217528\pi$
$234$	4893.88	+	3060.93i	0.0893762	+	0.0559013i
$235$	−35873.2			−0.649582
$236$	19495.5	−	19495.5i	0.350034	−	0.350034i
$237$	−12318.7			−0.219316
$238$			36036.3i			0.636189i
$239$	40406.7	−	40406.7i	0.707388	−	0.707388i	−0.258597	−	0.965985i	$-0.583260\pi$
$239$	40406.7	−	40406.7i	0.707388	−	0.707388i	0.965985	+	0.258597i	$0.0832603\pi$
$240$	−9611.07	+	9611.07i	−0.166859	+	0.166859i
$241$	−65853.8	−	65853.8i	−1.13383	−	1.13383i	−0.989535	−	0.144291i	$-0.953910\pi$
$241$	−65853.8	−	65853.8i	−1.13383	−	1.13383i	−0.144291	−	0.989535i	$-0.546090\pi$
$242$	−2300.64	−	2300.64i	−0.0392843	−	0.0392843i
$243$	−26464.8			−0.448184
$244$		−	11300.0i		−	0.189801i
$245$	17297.9	+	17297.9i	0.288178	+	0.288178i
$246$		−	14254.3i		−	0.235546i
$247$	−29528.1	−	18468.6i	−0.483995	−	0.302720i
$248$	72816.8			1.18394
$249$	−26139.0	+	26139.0i	−0.421590	+	0.421590i
$250$	−26132.1			−0.418114
$251$			11580.7i			0.183817i	0.995767	+	0.0919086i	$0.0292968\pi$
$251$			11580.7i			0.183817i	−0.995767	+	0.0919086i	$0.970703\pi$
$252$	10746.2	−	10746.2i	0.169221	−	0.169221i
$253$	−6546.73	+	6546.73i	−0.102278	+	0.102278i
$254$	−21792.5	−	21792.5i	−0.337785	−	0.337785i
$255$	27649.6	+	27649.6i	0.425214	+	0.425214i
$256$	−33846.5			−0.516456
$257$			112157.i			1.69808i	0.528325	+	0.849042i	$0.322820\pi$
$257$			112157.i			1.69808i	−0.528325	+	0.849042i	$0.677180\pi$
$258$	29764.6	+	29764.6i	0.447157	+	0.447157i
$259$		−	31922.8i		−	0.475885i
$260$	14805.1	−	23670.7i	0.219010	−	0.350158i
$261$	26973.9			0.395971
$262$	−28434.4	+	28434.4i	−0.414229	+	0.414229i
$263$	−49442.1			−0.714802			−0.357401	−	0.933951i	$-0.616337\pi$
$263$	−49442.1			−0.714802			−0.357401	+	0.933951i	$0.616337\pi$
$264$		−	67463.9i		−	0.967974i
$265$	40430.9	−	40430.9i	0.575734	−	0.575734i
$266$	17581.1	−	17581.1i	0.248475	−	0.248475i
$267$	28383.5	+	28383.5i	0.398147	+	0.398147i
$268$	28106.7	+	28106.7i	0.391327	+	0.391327i
$269$	48335.1			0.667972			0.333986	−	0.942578i	$-0.391606\pi$
$269$	48335.1			0.667972			0.333986	+	0.942578i	$0.391606\pi$
$270$		−	15118.5i		−	0.207387i
$271$	29110.8	+	29110.8i	0.396383	+	0.396383i	0.876955	−	0.480572i	$-0.159571\pi$
$271$	29110.8	+	29110.8i	0.396383	+	0.396383i	−0.480572	+	0.876955i	$0.659571\pi$
$272$		−	31011.8i		−	0.419169i
$273$	−58375.4	+	93331.8i	−0.783258	+	1.25229i
$274$	−2177.93			−0.0290097
$275$	−40999.8	+	40999.8i	−0.542146	+	0.542146i
$276$	−9076.07			−0.119146
$277$		−	122108.i		−	1.59142i	−0.605679	−	0.795709i	$-0.707098\pi$
$277$		−	122108.i		−	1.59142i	0.605679	−	0.795709i	$-0.292902\pi$
$278$	28331.9	−	28331.9i	0.366594	−	0.366594i
$279$	−18025.0	+	18025.0i	−0.231562	+	0.231562i
$280$	32008.7	+	32008.7i	0.408275	+	0.408275i
$281$	91868.7	+	91868.7i	1.16347	+	1.16347i	0.983711	+	0.179759i	$0.0575318\pi$
$281$	91868.7	+	91868.7i	1.16347	+	1.16347i	0.179759	+	0.983711i	$0.442468\pi$
$282$	50364.7			0.633327
$283$		−	19341.5i		−	0.241500i	−0.992683	−	0.120750i	$-0.961470\pi$
$283$		−	19341.5i		−	0.241500i	0.992683	−	0.120750i	$-0.0385299\pi$
$284$	−15331.1	−	15331.1i	−0.190080	−	0.190080i
$285$		−	26978.9i		−	0.332151i
$286$	8978.23	+	38964.6i	0.109764	+	0.476363i
$287$	50518.1			0.613314
$288$	13554.3	−	13554.3i	0.163416	−	0.163416i
$289$	−5695.00			−0.0681865
$290$			35376.2i			0.420644i
$291$	−41782.6	+	41782.6i	−0.493412	+	0.493412i
$292$	−20334.0	+	20334.0i	−0.238483	+	0.238483i
$293$	−73142.2	−	73142.2i	−0.851986	−	0.851986i	0.138391	−	0.990378i	$-0.455807\pi$
$293$	−73142.2	−	73142.2i	−0.851986	−	0.851986i	−0.990378	+	0.138391i	$0.955807\pi$
$294$	−24285.6	−	24285.6i	−0.280967	−	0.280967i
$295$	−28748.9			−0.330352
$296$		−	25815.8i		−	0.294647i
$297$	−56465.5	−	56465.5i	−0.640133	−	0.640133i
$298$		−	73622.2i		−	0.829041i
$299$	11905.3	−	2743.23i	0.133168	−	0.0306846i
$300$	−56840.1			−0.631557
$301$	−105487.	+	105487.i	−1.16431	+	1.16431i
$302$	39779.9			0.436164
$303$		−	106471.i		−	1.15970i
$304$	−15129.8	+	15129.8i	−0.163714	+	0.163714i
$305$	−8331.74	+	8331.74i	−0.0895645	+	0.0895645i
$306$	−7213.87	−	7213.87i	−0.0770416	−	0.0770416i
$307$	48488.0	+	48488.0i	0.514467	+	0.514467i	0.915892	−	0.401425i	$-0.131485\pi$
$307$	48488.0	+	48488.0i	0.514467	+	0.514467i	−0.401425	+	0.915892i	$0.631485\pi$
$308$	105275.			1.10975
$309$		−	131780.i		−	1.38017i
$310$	−23639.8	−	23639.8i	−0.245991	−	0.245991i
$311$			77566.8i			0.801965i	0.916086	+	0.400982i	$0.131331\pi$
$311$			77566.8i			0.801965i	−0.916086	+	0.400982i	$0.868669\pi$
$312$	−47207.7	+	75476.7i	−0.484958	+	0.775361i
$313$	−154244.			−1.57441			−0.787206	−	0.616690i	$-0.788473\pi$
$313$	−154244.			−1.57441			−0.787206	+	0.616690i	$0.788473\pi$
$314$	7365.93	−	7365.93i	0.0747082	−	0.0747082i
$315$	−15846.9			−0.159706
$316$		−	15545.5i		−	0.155679i
$317$	81584.8	−	81584.8i	0.811878	−	0.811878i	−0.173038	−	0.984915i	$-0.555358\pi$
$317$	81584.8	−	81584.8i	0.811878	−	0.811878i	0.984915	+	0.173038i	$0.0553582\pi$
$318$	−56763.6	+	56763.6i	−0.561327	+	0.561327i
$319$	132125.	+	132125.i	1.29838	+	1.29838i
$320$	2359.24	+	2359.24i	0.0230395	+	0.0230395i
$321$	−50359.4			−0.488732
$322$			8721.82i			0.0841193i
$323$	43526.1	+	43526.1i	0.417200	+	0.417200i
$324$		−	97130.7i		−	0.925266i
$325$	74558.9	−	17179.9i	0.705883	−	0.162650i
$326$	−59546.4			−0.560300
$327$	62048.4	−	62048.4i	0.580277	−	0.580277i
$328$	40853.6			0.379736
$329$			178495.i			1.64905i
$330$	−21902.0	+	21902.0i	−0.201120	+	0.201120i
$331$	117644.	−	117644.i	1.07378	−	1.07378i	0.0767231	−	0.997052i	$-0.475554\pi$
$331$	117644.	−	117644.i	1.07378	−	1.07378i	0.997052	−	0.0767231i	$-0.0244458\pi$
$332$	−32985.8	−	32985.8i	−0.299261	−	0.299261i
$333$	6390.43	+	6390.43i	0.0576290	+	0.0576290i
$334$	30300.7			0.271619
$335$		−	41447.4i		−	0.369324i
$336$	47822.0	+	47822.0i	0.423594	+	0.423594i
$337$		−	75439.4i		−	0.664260i	−0.943234	−	0.332130i	$-0.892233\pi$
$337$		−	75439.4i		−	0.664260i	0.943234	−	0.332130i	$-0.107767\pi$
$338$	17220.8	−	49874.9i	0.150737	−	0.436565i
$339$	109785.			0.955306
$340$	−34892.0	+	34892.0i	−0.301834	+	0.301834i
$341$	−176582.			−1.51858
$342$			7038.90i			0.0601800i
$343$	−24804.4	+	24804.4i	−0.210834	+	0.210834i
$344$	−85306.7	+	85306.7i	−0.720885	+	0.720885i
$345$	6691.99	+	6691.99i	0.0562234	+	0.0562234i
$346$	9491.85	+	9491.85i	0.0792864	+	0.0792864i
$347$	−20140.8			−0.167270			−0.0836349	−	0.996496i	$-0.526653\pi$
$347$	−20140.8			−0.167270			−0.0836349	+	0.996496i	$0.526653\pi$
$348$			183171.i			1.51251i
$349$	−39641.5	−	39641.5i	−0.325461	−	0.325461i	0.525396	−	0.850858i	$-0.323917\pi$
$349$	−39641.5	−	39641.5i	−0.325461	−	0.325461i	−0.850858	+	0.525396i	$0.823917\pi$
$350$			54621.6i			0.445891i
$351$	23660.4	+	102684.i	0.192047	+	0.833464i
$352$	132785.			1.07168
$353$	109698.	−	109698.i	0.880337	−	0.880337i	−0.113232	−	0.993569i	$-0.536120\pi$
$353$	109698.	−	109698.i	0.880337	−	0.880337i	0.993569	+	0.113232i	$0.0361202\pi$
$354$	40362.5			0.322086
$355$			22607.9i			0.179393i
$356$	−35818.2	+	35818.2i	−0.282620	+	0.282620i
$357$	137577.	−	137577.i	1.07946	−	1.07946i
$358$	−24436.2	−	24436.2i	−0.190663	−	0.190663i
$359$	−64675.4	−	64675.4i	−0.501823	−	0.501823i	0.410181	−	0.912004i	$-0.365465\pi$
$359$	−64675.4	−	64675.4i	−0.501823	−	0.501823i	−0.912004	+	0.410181i	$0.865465\pi$
$360$	−12815.2			−0.0988830
$361$			87850.6i			0.674109i
$362$	−19505.2	−	19505.2i	−0.148844	−	0.148844i
$363$			17566.4i			0.133312i
$364$	−117779.	−	73666.0i	−0.888923	−	0.555987i
$365$	29985.4			0.225074
$366$	11697.5	−	11697.5i	0.0873232	−	0.0873232i
$367$	−76091.9			−0.564945			−0.282473	−	0.959275i	$-0.591155\pi$
$367$	−76091.9			−0.564945			−0.282473	+	0.959275i	$0.591155\pi$
$368$		−	7505.75i		−	0.0554241i
$369$	−10112.9	+	10112.9i	−0.0742715	+	0.0742715i
$370$	−8381.02	+	8381.02i	−0.0612200	+	0.0612200i
$371$	−201173.	−	201173.i	−1.46158	−	1.46158i
$372$	−122402.	−	122402.i	−0.884513	−	0.884513i
$373$	−71517.3			−0.514036			−0.257018	−	0.966407i	$-0.582740\pi$
$373$	−71517.3			−0.514036			−0.257018	+	0.966407i	$0.582740\pi$
$374$		−	70670.5i		−	0.505237i
$375$	99765.3	+	99765.3i	0.709442	+	0.709442i
$376$			144347.i			1.02102i
$377$	−55363.4	−	240271.i	−0.389529	−	1.69052i
$378$	−75225.7			−0.526481
$379$	28771.4	−	28771.4i	0.200301	−	0.200301i	−0.599828	−	0.800129i	$-0.704764\pi$
$379$	28771.4	−	28771.4i	0.200301	−	0.200301i	0.800129	+	0.599828i	$0.204764\pi$
$380$	34045.7			0.235774
$381$			166396.i			1.14628i
$382$	44803.8	−	44803.8i	0.307035	−	0.307035i
$383$	−64468.1	+	64468.1i	−0.439488	+	0.439488i	−0.891840	−	0.452352i	$-0.850585\pi$
$383$	−64468.1	+	64468.1i	−0.439488	+	0.439488i	0.452352	+	0.891840i	$0.350585\pi$
$384$	113689.	+	113689.i	0.771000	+	0.771000i
$385$	−77621.8	−	77621.8i	−0.523675	−	0.523675i
$386$	13176.9			0.0884379
$387$		−	42233.6i		−	0.281992i
$388$	−52727.0	−	52727.0i	−0.350243	−	0.350243i
$389$			220659.i			1.45822i	0.684397	+	0.729110i	$0.260066\pi$
$389$			220659.i			1.45822i	−0.684397	+	0.729110i	$0.739934\pi$
$390$	39829.2	−	9177.45i	0.261862	−	0.0603382i
$391$	−21592.9			−0.141240
$392$	69603.7	−	69603.7i	0.452961	−	0.452961i
$393$	217109.			1.40570
$394$		−	24279.5i		−	0.156404i
$395$	−11462.0	+	11462.0i	−0.0734627	+	0.0734627i
$396$	−21074.3	+	21074.3i	−0.134389	+	0.134389i
$397$	96072.7	+	96072.7i	0.609563	+	0.609563i	0.942832	−	0.333269i	$-0.108152\pi$
$397$	96072.7	+	96072.7i	0.609563	+	0.609563i	−0.333269	+	0.942832i	$0.608152\pi$
$398$	−12197.6	−	12197.6i	−0.0770029	−	0.0770029i
$399$	−134240.			−0.843209
$400$		−	47005.8i		−	0.293786i
$401$	−3174.38	−	3174.38i	−0.0197410	−	0.0197410i	0.697167	−	0.716908i	$-0.254443\pi$
$401$	−3174.38	−	3174.38i	−0.0197410	−	0.0197410i	−0.716908	+	0.697167i	$0.754443\pi$
$402$			58190.7i			0.360082i
$403$	197555.	+	123563.i	1.21640	+	0.760813i
$404$	134360.			0.823201
$405$	−71616.7	+	71616.7i	−0.436621	+	0.436621i
$406$	176022.			1.06786
$407$			62603.7i			0.377930i
$408$	111257.	−	111257.i	0.668355	−	0.668355i
$409$	46288.7	−	46288.7i	0.276712	−	0.276712i	−0.555083	−	0.831795i	$-0.687313\pi$
$409$	46288.7	−	46288.7i	0.276712	−	0.276712i	0.831795	+	0.555083i	$0.187313\pi$
$410$	−13263.0	−	13263.0i	−0.0788995	−	0.0788995i
$411$	8314.73	+	8314.73i	0.0492226	+	0.0492226i
$412$	166298.			0.979701
$413$			143047.i			0.838644i
$414$	−1745.96	−	1745.96i	−0.0101867	−	0.0101867i
$415$			48642.3i			0.282435i
$416$	−148556.	−	92915.9i	−0.858426	−	0.536912i
$417$	−216327.			−1.24405
$418$	−34478.2	+	34478.2i	−0.197330	+	0.197330i
$419$	67972.5			0.387173			0.193586	−	0.981083i	$-0.437988\pi$
$419$	67972.5			0.387173			0.193586	+	0.981083i	$0.437988\pi$
$420$		−	107611.i		−	0.610040i
$421$	−187465.	+	187465.i	−1.05768	+	1.05768i	−0.0594522	+	0.998231i	$0.518935\pi$
$421$	−187465.	+	187465.i	−1.05768	+	1.05768i	−0.998231	+	0.0594522i	$0.981065\pi$
$422$	−70301.3	+	70301.3i	−0.394765	+	0.394765i
$423$	−35731.7	−	35731.7i	−0.199698	−	0.199698i
$424$	−162687.	−	162687.i	−0.904943	−	0.904943i
$425$	−135228.			−0.748669
$426$		−	31740.8i		−	0.174903i
$427$	41456.4	+	41456.4i	0.227371	+	0.227371i
$428$		−	63550.4i		−	0.346921i
$429$	114480.	−	183032.i	0.622033	−	0.994520i
$430$	55389.2			0.299563
$431$	66845.4	−	66845.4i	0.359846	−	0.359846i	−0.503910	−	0.863756i	$-0.668106\pi$
$431$	66845.4	−	66845.4i	0.359846	−	0.359846i	0.863756	+	0.503910i	$0.168106\pi$
$432$	64737.0			0.346885
$433$		−	186395.i		−	0.994166i	−0.867703	−	0.497083i	$-0.834404\pi$
$433$		−	186395.i		−	0.994166i	0.867703	−	0.497083i	$-0.165596\pi$
$434$	−117625.	+	117625.i	−0.624482	+	0.624482i
$435$	135057.	−	135057.i	0.713735	−	0.713735i
$436$	78301.1	+	78301.1i	0.411903	+	0.411903i
$437$	10534.6	+	10534.6i	0.0551638	+	0.0551638i
$438$	−42098.5			−0.219441
$439$		−	106639.i		−	0.553333i	−0.960966	−	0.276667i	$-0.910770\pi$
$439$		−	106639.i		−	0.553333i	0.960966	−	0.276667i	$-0.0892297\pi$
$440$	−62772.1	−	62772.1i	−0.324236	−	0.324236i
$441$			34459.4i			0.177186i
$442$	−49451.5	+	79064.1i	−0.253125	+	0.404702i
$443$	90694.5			0.462140			0.231070	−	0.972937i	$-0.425777\pi$
$443$	90694.5			0.462140			0.231070	+	0.972937i	$0.425777\pi$
$444$	−43395.4	+	43395.4i	−0.220129	+	0.220129i
$445$	52819.1			0.266730
$446$			70973.3i			0.356800i
$447$	−281069.	+	281069.i	−1.40669	+	1.40669i
$448$	11738.9	−	11738.9i	0.0584888	−	0.0584888i
$449$	53532.0	+	53532.0i	0.265534	+	0.265534i	0.827298	−	0.561764i	$-0.189877\pi$
$449$	53532.0	+	53532.0i	0.265534	+	0.265534i	−0.561764	+	0.827298i	$0.689877\pi$
$450$	−10934.3	−	10934.3i	−0.0539968	−	0.0539968i
$451$	−99070.7			−0.487071
$452$			138541.i			0.678114i
$453$	−151869.	−	151869.i	−0.740069	−	0.740069i
$454$		−	165880.i		−	0.804789i
$455$	32525.3	+	141157.i	0.157108	+	0.681834i
$456$	−108559.			−0.522077
$457$	21404.9	−	21404.9i	0.102490	−	0.102490i	−0.654003	−	0.756492i	$-0.726911\pi$
$457$	21404.9	−	21404.9i	0.102490	−	0.102490i	0.756492	+	0.654003i	$0.226911\pi$
$458$	−55513.8			−0.264649
$459$		−	186238.i		−	0.883982i
$460$	−8444.87	+	8444.87i	−0.0399096	+	0.0399096i
$461$	225398.	−	225398.i	1.06059	−	1.06059i	0.0625486	−	0.998042i	$-0.480077\pi$
$461$	225398.	−	225398.i	1.06059	−	1.06059i	0.998042	−	0.0625486i	$-0.0199228\pi$
$462$	108978.	+	108978.i	0.510571	+	0.510571i
$463$	1729.47	+	1729.47i	0.00806774	+	0.00806774i	0.711129	−	0.703061i	$-0.248184\pi$
$463$	1729.47	+	1729.47i	0.00806774	+	0.00806774i	−0.703061	+	0.711129i	$0.748184\pi$
$464$	−151480.			−0.703587
$465$			180500.i			0.834780i
$466$	9685.45	+	9685.45i	0.0446014	+	0.0446014i
$467$		−	131914.i		−	0.604864i	−0.953171	−	0.302432i	$-0.902201\pi$
$467$		−	131914.i		−	0.604864i	0.953171	−	0.302432i	$-0.0977985\pi$
$468$	38324.1	−	8830.64i	0.174977	−	0.0403182i
$469$	−206231.			−0.937578
$470$	46862.0	−	46862.0i	0.212141	−	0.212141i
$471$	−56242.2			−0.253525
$472$			115681.i			0.519251i
$473$	206870.	−	206870.i	0.924647	−	0.924647i
$474$	16092.3	−	16092.3i	0.0716243	−	0.0716243i
$475$	65974.2	+	65974.2i	0.292406	+	0.292406i
$476$	173613.	+	173613.i	0.766245	+	0.766245i
$477$	80543.0			0.353990
$478$			105569.i			0.462039i
$479$	113839.	+	113839.i	0.496158	+	0.496158i	0.910240	−	0.414082i	$-0.135897\pi$
$479$	113839.	+	113839.i	0.496158	+	0.496158i	−0.414082	+	0.910240i	$0.635897\pi$
$480$		−	135731.i		−	0.589111i
$481$	43806.8	−	70039.2i	0.189344	−	0.302727i
$482$	172053.			0.740573
$483$	33297.5	−	33297.5i	0.142731	−	0.142731i
$484$	−22167.7			−0.0946304
$485$			77753.7i			0.330550i
$486$	34571.6	−	34571.6i	0.146368	−	0.146368i
$487$	−252418.	+	252418.i	−1.06430	+	1.06430i	−0.0665104	+	0.997786i	$0.521187\pi$
$487$	−252418.	+	252418.i	−1.06430	+	1.06430i	−0.997786	+	0.0665104i	$0.978813\pi$
$488$	33525.5	+	33525.5i	0.140778	+	0.140778i
$489$	227332.	+	227332.i	0.950698	+	0.950698i
$490$	−45193.3			−0.188227
$491$		−	336665.i		−	1.39648i	−0.715864	−	0.698240i	$-0.753967\pi$
$491$		−	336665.i		−	1.39648i	0.715864	−	0.698240i	$-0.246033\pi$
$492$	−68673.4	−	68673.4i	−0.283699	−	0.283699i
$493$			435783.i			1.79298i
$494$	62699.3	−	14447.2i	0.256926	−	0.0592010i
$495$	31077.2			0.126833
$496$	101225.	−	101225.i	0.411455	−	0.411455i
$497$	112491.			0.455412
$498$		−	68292.1i		−	0.275367i
$499$	239050.	−	239050.i	0.960036	−	0.960036i	−0.0391952	−	0.999232i	$-0.512479\pi$
$499$	239050.	−	239050.i	0.960036	−	0.960036i	0.999232	+	0.0391952i	$0.0124794\pi$
$500$	−125897.	+	125897.i	−0.503590	+	0.503590i
$501$	−115680.	−	115680.i	−0.460874	−	0.460874i
$502$	−15128.1	−	15128.1i	−0.0600313	−	0.0600313i
$503$	27136.5			0.107255			0.0536276	−	0.998561i	$-0.482922\pi$
$503$	27136.5			0.107255			0.0536276	+	0.998561i	$0.482922\pi$
$504$			63765.1i			0.251028i
$505$	−99066.4	−	99066.4i	−0.388458	−	0.388458i
$506$		−	17104.3i		−	0.0668043i
$507$	−256153.	+	124665.i	−0.996514	+	0.484984i
$508$	−209981.			−0.813677
$509$	−193359.	+	193359.i	−0.746325	+	0.746325i	−0.973787	−	0.227462i	$-0.926957\pi$
$509$	−193359.	+	193359.i	−0.746325	+	0.746325i	0.227462	+	0.973787i	$0.426957\pi$
$510$	−72238.6			−0.277734
$511$		−	149199.i		−	0.571380i
$512$	−138154.	+	138154.i	−0.527017	+	0.527017i
$513$	−90860.6	+	90860.6i	−0.345256	+	0.345256i
$514$	−146513.	−	146513.i	−0.554563	−	0.554563i
$515$	−122616.	−	122616.i	−0.462308	−	0.462308i
$516$	286795.			1.07714
$517$		−	350045.i		−	1.30961i
$518$	41701.6	+	41701.6i	0.155415	+	0.155415i
$519$		−	72474.5i		−	0.269061i
$520$	26303.0	+	114152.i	0.0972744	+	0.422161i
$521$	436420.			1.60779			0.803895	−	0.594772i	$-0.202758\pi$
$521$	436420.			1.60779			0.803895	+	0.594772i	$0.202758\pi$
$522$	−35236.7	+	35236.7i	−0.129317	+	0.129317i
$523$	−405280.			−1.48167			−0.740835	−	0.671687i	$-0.765570\pi$
$523$	−405280.			−1.48167			−0.740835	+	0.671687i	$0.765570\pi$
$524$			273978.i			0.997821i
$525$	208530.	−	208530.i	0.756572	−	0.756572i
$526$	64587.5	−	64587.5i	0.233441	−	0.233441i
$527$	−291207.	−	291207.i	−1.04853	−	1.04853i
$528$	−93783.5	−	93783.5i	−0.336402	−	0.336402i
$529$	274615.			0.981325
$530$			105632.i			0.376048i
$531$	−28635.6	−	28635.6i	−0.101559	−	0.101559i
$532$		−	169402.i		−	0.598543i
$533$	110837.	+	69324.5i	0.390150	+	0.244024i
$534$	−74156.2			−0.260055
$535$	−46857.1	+	46857.1i	−0.163707	+	0.163707i
$536$	−166777.			−0.580506
$537$			186581.i			0.647022i
$538$	−63141.4	+	63141.4i	−0.218147	+	0.218147i
$539$	−168790.	+	168790.i	−0.580992	+	0.580992i
$540$	−72837.0	−	72837.0i	−0.249784	−	0.249784i
$541$	−16926.3	−	16926.3i	−0.0578320	−	0.0578320i	0.677599	−	0.735431i	$-0.263020\pi$
$541$	−16926.3	−	16926.3i	−0.0578320	−	0.0578320i	−0.735431	+	0.677599i	$0.763020\pi$
$542$	−76056.2			−0.258902
$543$			148931.i			0.505108i
$544$	218980.	+	218980.i	0.739957	+	0.739957i
$545$		−	115466.i		−	0.388743i
$546$	−45664.4	−	198179.i	−0.153177	−	0.664771i
$547$	249610.			0.834234			0.417117	−	0.908853i	$-0.363041\pi$
$547$	249610.			0.834234			0.417117	+	0.908853i	$0.363041\pi$
$548$	−10492.7	+	10492.7i	−0.0349401	+	0.0349401i
$549$	−16597.8			−0.0550688
$550$		−	107118.i		−	0.354109i
$551$	212607.	−	212607.i	0.700283	−	0.700283i
$552$	26927.4	−	26927.4i	0.0883724	−	0.0883724i
$553$	57031.8	+	57031.8i	0.186495	+	0.186495i
$554$	159513.	+	159513.i	0.519728	+	0.519728i
$555$	63992.8			0.207752
$556$		−	272990.i		−	0.883075i
$557$	294084.	+	294084.i	0.947896	+	0.947896i	0.998708	−	0.0508124i	$-0.0161811\pi$
$557$	294084.	+	294084.i	0.947896	+	0.947896i	−0.0508124	+	0.998708i	$0.516181\pi$
$558$		−	47093.1i		−	0.151248i
$559$	−376198.	+	86683.5i	−1.20391	+	0.277404i
$560$	88992.5			0.283777
$561$	−269800.	+	269800.i	−0.857269	+	0.857269i
$562$	−240021.			−0.759935
$563$		−	196107.i		−	0.618694i	−0.950949	−	0.309347i	$-0.899890\pi$
$563$		−	196107.i		−	0.618694i	0.950949	−	0.309347i	$-0.100110\pi$
$564$	242643.	−	242643.i	0.762798	−	0.762798i
$565$	102150.	−	102150.i	0.319993	−	0.319993i
$566$	25266.3	+	25266.3i	0.0788693	+	0.0788693i
$567$	356345.	+	356345.i	1.10842	+	1.10842i
$568$	90970.5			0.281971
$569$			446515.i			1.37915i	0.724215	+	0.689575i	$0.242202\pi$
$569$			446515.i			1.37915i	−0.724215	+	0.689575i	$0.757798\pi$
$570$	35243.3	+	35243.3i	0.108474	+	0.108474i
$571$		−	337194.i		−	1.03421i	−0.855922	−	0.517104i	$-0.827010\pi$
$571$		−	337194.i		−	1.03421i	0.855922	−	0.517104i	$-0.172990\pi$
$572$	230975.	+	144466.i	0.705949	+	0.441544i
$573$	−342097.			−1.04194
$574$	−65993.0	+	65993.0i	−0.200297	+	0.200297i
$575$	−32729.2			−0.0989918
$576$			4699.88i			0.0141658i
$577$	−111217.	+	111217.i	−0.334055	+	0.334055i	−0.854124	−	0.520069i	$-0.825906\pi$
$577$	−111217.	+	111217.i	−0.334055	+	0.334055i	0.520069	+	0.854124i	$0.325906\pi$
$578$	7439.52	−	7439.52i	0.0222684	−	0.0222684i
$579$	−50305.8	−	50305.8i	−0.150058	−	0.150058i
$580$	170433.	+	170433.i	0.506637	+	0.506637i
$581$	242031.			0.716998
$582$		−	109163.i		−	0.322278i
$583$	394519.	+	394519.i	1.16073	+	1.16073i
$584$		−	120656.i		−	0.353772i
$585$	−34768.3	−	21746.2i	−0.101595	−	0.0635435i
$586$	191095.			0.556486
$587$	36868.8	−	36868.8i	0.107000	−	0.107000i	−0.651580	−	0.758580i	$-0.725894\pi$
$587$	36868.8	−	36868.8i	0.107000	−	0.107000i	0.758580	+	0.651580i	$0.225894\pi$
$588$	−234003.			−0.676810
$589$			284144.i			0.819046i
$590$	37555.4	−	37555.4i	0.107887	−	0.107887i
$591$	−92692.3	+	92692.3i	−0.265380	+	0.265380i
$592$	−35887.2	−	35887.2i	−0.102399	−	0.102399i
$593$	−404224.	−	404224.i	−1.14951	−	1.14951i	−0.986649	−	0.162862i	$-0.947928\pi$
$593$	−404224.	−	404224.i	−1.14951	−	1.14951i	−0.162862	−	0.986649i	$-0.552072\pi$
$594$	147525.			0.418111
$595$		−	256017.i		−	0.723162i
$596$	−354691.	−	354691.i	−0.998523	−	0.998523i
$597$			93133.9i			0.261312i
$598$	−11968.7	+	19135.8i	−0.0334691	+	0.0535112i
$599$	−593378.			−1.65378			−0.826890	−	0.562363i	$-0.809892\pi$
$599$	−593378.			−1.65378			−0.826890	+	0.562363i	$0.809892\pi$
$600$	168637.	−	168637.i	0.468435	−	0.468435i
$601$	213129.			0.590057			0.295029	−	0.955488i	$-0.404671\pi$
$601$	213129.			0.590057			0.295029	+	0.955488i	$0.404671\pi$
$602$		−	275601.i		−	0.760481i
$603$	41284.0	−	41284.0i	0.113539	−	0.113539i
$604$	191649.	−	191649.i	0.525330	−	0.525330i
$605$	16344.8	+	16344.8i	0.0446548	+	0.0446548i
$606$	139086.	+	139086.i	0.378737	+	0.378737i
$607$	−342979.			−0.930871			−0.465436	−	0.885082i	$-0.654102\pi$
$607$	−342979.			−0.930871			−0.465436	+	0.885082i	$0.654102\pi$
$608$		−	213669.i		−	0.578008i
$609$	−672004.	−	672004.i	−1.81191	−	1.81191i
$610$		−	21767.9i		−	0.0585002i
$611$	−244943.	+	391621.i	−0.656120	+	1.04902i
$612$	−69508.8			−0.185583
$613$	48611.1	−	48611.1i	0.129364	−	0.129364i	−0.639460	−	0.768824i	$-0.720842\pi$
$613$	48611.1	−	48611.1i	0.129364	−	0.129364i	0.768824	+	0.639460i	$0.220842\pi$
$614$	−126682.			−0.336031
$615$			101269.i			0.267748i
$616$	−312337.	+	312337.i	−0.823117	+	0.823117i
$617$	−1700.28	+	1700.28i	−0.00446632	+	0.00446632i	−0.709336	−	0.704870i	$-0.751005\pi$
$617$	−1700.28	+	1700.28i	−0.00446632	+	0.00446632i	0.704870	+	0.709336i	$0.251005\pi$
$618$	172148.	+	172148.i	0.450739	+	0.450739i
$619$	332782.	+	332782.i	0.868518	+	0.868518i	0.992308	−	0.123790i	$-0.0395051\pi$
$619$	332782.	+	332782.i	0.868518	+	0.868518i	−0.123790	+	0.992308i	$0.539505\pi$
$620$	−227780.			−0.592559
$621$		−	45075.1i		−	0.116884i
$622$	−101328.	−	101328.i	−0.261907	−	0.261907i
$623$		−	262813.i		−	0.677129i
$624$	39297.5	+	170547.i	0.100924	+	0.438001i
$625$	−97306.5			−0.249105
$626$	201492.	−	201492.i	0.514173	−	0.514173i
$627$	263257.			0.669645
$628$		−	70974.0i		−	0.179962i
$629$	−103242.	+	103242.i	−0.260948	+	0.260948i
$630$	20701.2	−	20701.2i	0.0521571	−	0.0521571i
$631$	282632.	+	282632.i	0.709845	+	0.709845i	0.966502	−	0.256658i	$-0.0826213\pi$
$631$	282632.	+	282632.i	0.709845	+	0.709845i	−0.256658	+	0.966502i	$0.582621\pi$
$632$	46121.2	+	46121.2i	0.115469	+	0.115469i
$633$	536782.			1.33965
$634$			213152.i			0.530288i
$635$	154824.	+	154824.i	0.383963	+	0.383963i
$636$			546943.i			1.35216i
$637$	306949.	−	70727.1i	0.756461	−	0.174304i
$638$	−345196.			−0.848055
$639$	−22518.8	+	22518.8i	−0.0551498	+	0.0551498i
$640$	211564.			0.516514
$641$		−	396296.i		−	0.964502i	−0.876033	−	0.482251i	$-0.839819\pi$
$641$		−	396296.i		−	0.964502i	0.876033	−	0.482251i	$-0.160181\pi$
$642$	65785.8	−	65785.8i	0.159611	−	0.159611i
$643$	−269894.	+	269894.i	−0.652787	+	0.652787i	−0.953663	−	0.300876i	$-0.902721\pi$
$643$	−269894.	+	269894.i	−0.652787	+	0.652787i	0.300876	+	0.953663i	$0.402721\pi$
$644$	42019.3	+	42019.3i	0.101316	+	0.101316i
$645$	−211461.	−	211461.i	−0.508288	−	0.508288i
$646$	−113718.			−0.272500
$647$		−	420499.i		−	1.00451i	−0.864718	−	0.502257i	$-0.832503\pi$
$647$		−	420499.i		−	1.00451i	0.864718	−	0.502257i	$-0.167497\pi$
$648$	288173.	+	288173.i	0.686284	+	0.686284i
$649$		−	280528.i		−	0.666019i
$650$	−74955.6	+	119841.i	−0.177410	+	0.283646i
$651$	898119.			2.11920
$652$	−286878.	+	286878.i	−0.674843	+	0.674843i
$653$	22664.5			0.0531519			0.0265760	−	0.999647i	$-0.491540\pi$
$653$	22664.5			0.0531519			0.0265760	+	0.999647i	$0.491540\pi$
$654$			162111.i			0.379015i
$655$	202010.	−	202010.i	0.470858	−	0.470858i
$656$	56791.7	−	56791.7i	0.131971	−	0.131971i
$657$	29867.2	+	29867.2i	0.0691933	+	0.0691933i
$658$	−233173.	−	233173.i	−0.538549	−	0.538549i
$659$	−298784.			−0.687998			−0.343999	−	0.938970i	$-0.611782\pi$
$659$	−298784.			−0.687998			−0.343999	+	0.938970i	$0.611782\pi$
$660$			211035.i			0.484471i
$661$	−451526.	−	451526.i	−1.03343	−	1.03343i	−0.999422	−	0.0340055i	$-0.989174\pi$
$661$	−451526.	−	451526.i	−1.03343	−	1.03343i	−0.0340055	−	0.999422i	$-0.510826\pi$
$662$			307362.i			0.701350i
$663$	490637.	−	113053.i	1.11618	−	0.257190i
$664$	195728.			0.443933
$665$	−124904.	+	124904.i	−0.282444	+	0.282444i
$666$	−16695.9			−0.0376411
$667$			105472.i			0.237075i
$668$	145981.	−	145981.i	0.327146	−	0.327146i
$669$	270957.	−	270957.i	0.605407	−	0.605407i
$670$	54143.7	+	54143.7i	0.120614	+	0.120614i
$671$	−81299.9	−	81299.9i	−0.180570	−	0.180570i
$672$	−675361.			−1.49554
$673$			740886.i			1.63577i	0.575384	+	0.817883i	$0.304852\pi$
$673$			740886.i			1.63577i	−0.575384	+	0.817883i	$0.695148\pi$
$674$	98548.4	+	98548.4i	0.216935	+	0.216935i
$675$		−	282289.i		−	0.619564i
$676$	−157319.	−	323249.i	−0.344260	−	0.707365i
$677$	−220043.			−0.480099			−0.240050	−	0.970761i	$-0.577164\pi$
$677$	−220043.			−0.480099			−0.240050	+	0.970761i	$0.577164\pi$
$678$	−143415.	+	143415.i	−0.311985	+	0.311985i
$679$	386881.			0.839146
$680$		−	207039.i		−	0.447749i
$681$	−633284.	+	633284.i	−1.36554	+	1.36554i
$682$	230674.	−	230674.i	0.495940	−	0.495940i
$683$	472955.	+	472955.i	1.01386	+	1.01386i	0.999903	+	0.0139589i	$0.00444341\pi$
$683$	472955.	+	472955.i	1.01386	+	1.01386i	0.0139589	+	0.999903i	$0.495557\pi$
$684$	33911.5	+	33911.5i	0.0724827	+	0.0724827i
$685$	15473.0			0.0329756
$686$		−	64805.1i		−	0.137709i
$687$	211936.	+	211936.i	0.449047	+	0.449047i
$688$			237174.i			0.501062i
$689$	−165313.	−	717441.i	−0.348231	−	1.51129i
$690$	−17483.8			−0.0367230
$691$	423991.	−	423991.i	0.887974	−	0.887974i	−0.106354	−	0.994328i	$-0.533918\pi$
$691$	423991.	−	423991.i	0.887974	−	0.887974i	0.994328	+	0.106354i	$0.0339176\pi$
$692$	91458.2			0.190990
$693$		−	154632.i		−	0.321982i
$694$	26310.4	−	26310.4i	0.0546272	−	0.0546272i
$695$	−201282.	+	201282.i	−0.416711	+	0.416711i
$696$	−543444.	−	543444.i	−1.12185	−	1.12185i
$697$	−163381.	−	163381.i	−0.336307	−	0.336307i
$698$	103569.			0.212579
$699$		−	73952.8i		−	0.151356i
$700$	263152.	+	263152.i	0.537045	+	0.537045i
$701$			298102.i			0.606637i	0.952889	+	0.303318i	$0.0980946\pi$
$701$			298102.i			0.606637i	−0.952889	+	0.303318i	$0.901905\pi$
$702$	−165046.	−	103230.i	−0.334913	−	0.209475i
$703$	100738.			0.203836
$704$	−23021.1	+	23021.1i	−0.0464495	+	0.0464495i
$705$	−357813.			−0.719909
$706$			286602.i			0.575003i
$707$	−492927.	+	492927.i	−0.986152	+	0.986152i
$708$	194455.	−	194455.i	0.387930	−	0.387930i
$709$	−605423.	−	605423.i	−1.20439	−	1.20439i	−0.972818	−	0.231570i	$-0.925614\pi$
$709$	−605423.	−	605423.i	−1.20439	−	1.20439i	−0.231570	−	0.972818i	$-0.574386\pi$
$710$	−29533.3	−	29533.3i	−0.0585862	−	0.0585862i
$711$	−22833.7			−0.0451686
$712$		−	212535.i		−	0.419248i
$713$	−70480.6	−	70480.6i	−0.138641	−	0.138641i
$714$			359439.i			0.705065i
$715$	−63785.2	−	276821.i	−0.124769	−	0.541486i
$716$	−235453.			−0.459281
$717$	403032.	−	403032.i	0.783973	−	0.783973i
$718$	168974.			0.327772
$719$		−	9526.58i		−	0.0184281i	−0.999958	−	0.00921403i	$-0.997067\pi$
$719$		−	9526.58i		−	0.0184281i	0.999958	−	0.00921403i	$-0.00293296\pi$
$720$	−17814.8	+	17814.8i	−0.0343650	+	0.0343650i
$721$	−610101.	+	610101.i	−1.17363	+	1.17363i
$722$	−114761.	−	114761.i	−0.220152	−	0.220152i
$723$	−656850.	−	656850.i	−1.25658	−	1.25658i
$724$	−187941.			−0.358545
$725$			660533.i			1.25666i
$726$	−22947.5	−	22947.5i	−0.0435373	−	0.0435373i
$727$			502918.i			0.951543i	0.879569	+	0.475771i	$0.157831\pi$
$727$			502918.i			0.951543i	−0.879569	+	0.475771i	$0.842169\pi$
$728$	567990.	−	130876.i	1.07171	−	0.246944i
$729$	361085.			0.679446
$730$	−39170.7	+	39170.7i	−0.0735048	+	0.0735048i
$731$	682314.			1.27688
$732$		−	112710.i		−	0.210350i
$733$	400336.	−	400336.i	0.745103	−	0.745103i	−0.228452	−	0.973555i	$-0.573366\pi$
$733$	400336.	−	400336.i	0.745103	−	0.745103i	0.973555	+	0.228452i	$0.0733664\pi$
$734$	99400.8	−	99400.8i	0.184501	−	0.184501i
$735$	172536.	+	172536.i	0.319378	+	0.319378i
$736$	52999.5	+	52999.5i	0.0978400	+	0.0978400i
$737$	404438.			0.744589
$738$		−	26421.4i		−	0.0485114i
$739$	−111403.	−	111403.i	−0.203990	−	0.203990i	0.597717	−	0.801707i	$-0.296075\pi$
$739$	−111403.	−	111403.i	−0.203990	−	0.203990i	−0.801707	+	0.597717i	$0.796075\pi$
$740$			80754.8i			0.147471i
$741$	−294524.	−	184213.i	−0.536394	−	0.335494i
$742$	525595.			0.954648
$743$	255155.	−	255155.i	0.462196	−	0.462196i	−0.437179	−	0.899375i	$-0.644022\pi$
$743$	255155.	−	255155.i	0.462196	−	0.462196i	0.899375	+	0.437179i	$0.144022\pi$
$744$	726302.			1.31211
$745$			523044.i			0.942379i
$746$	93424.9	−	93424.9i	0.167875	−	0.167875i
$747$	−48450.5	+	48450.5i	−0.0868275	+	0.0868275i
$748$	−340471.	−	340471.i	−0.608523	−	0.608523i
$749$	233148.	+	233148.i	0.415593	+	0.415593i
$750$	−260652.			−0.463381
$751$			272472.i			0.483106i	0.970388	+	0.241553i	$0.0776568\pi$
$751$			272472.i			0.483106i	−0.970388	+	0.241553i	$0.922343\pi$
$752$	200661.	+	200661.i	0.354837	+	0.354837i
$753$			115510.i			0.203718i
$754$	386195.	+	241550.i	0.679304	+	0.424878i
$755$	−282614.			−0.495792
$756$	−362417.	+	362417.i	−0.634110	+	0.634110i
$757$	−136228.			−0.237725			−0.118862	−	0.992911i	$-0.537925\pi$
$757$	−136228.			−0.237725			−0.118862	+	0.992911i	$0.537925\pi$
$758$			75169.7i			0.130829i
$759$	−65299.5	+	65299.5i	−0.113351	+	0.113351i
$760$	−101009.	+	101009.i	−0.174877	+	0.174877i
$761$	815054.	+	815054.i	1.40740	+	1.40740i	0.773033	+	0.634366i	$0.218739\pi$
$761$	815054.	+	815054.i	1.40740	+	1.40740i	0.634366	+	0.773033i	$0.281261\pi$
$762$	−217367.	−	217367.i	−0.374355	−	0.374355i
$763$	−574529.			−0.986877
$764$		−	431705.i		−	0.739606i
$765$	51250.4	+	51250.4i	0.0875739	+	0.0875739i
$766$		−	168433.i		−	0.287057i
$767$	−196299.	+	313847.i	−0.333677	+	0.533490i
$768$	−337598.			−0.572370
$769$	494798.	−	494798.i	0.836710	−	0.836710i	−0.151714	−	0.988424i	$-0.548479\pi$
$769$	494798.	−	494798.i	0.836710	−	0.836710i	0.988424	+	0.151714i	$0.0484793\pi$
$770$	202799.			0.342045
$771$			1.11869e6i			1.88193i
$772$	63482.6	−	63482.6i	0.106517	−	0.106517i
$773$	536178.	−	536178.i	0.897325	−	0.897325i	−0.0978738	−	0.995199i	$-0.531204\pi$
$773$	536178.	−	536178.i	0.897325	−	0.897325i	0.995199	+	0.0978738i	$0.0312042\pi$
$774$	55170.8	+	55170.8i	0.0920932	+	0.0920932i
$775$	−441395.	−	441395.i	−0.734892	−	0.734892i
$776$	312867.			0.519561
$777$		−	318411.i		−	0.527406i
$778$	−288253.	−	288253.i	−0.476227	−	0.476227i
$779$			159418.i			0.262702i
$780$	147672.	−	236100.i	0.242721	−	0.388068i
$781$	−220605.			−0.361671
$782$	28207.3	−	28207.3i	0.0461262	−	0.0461262i
$783$	−909696.			−1.48379
$784$		−	193516.i		−	0.314837i
$785$	−52330.8	+	52330.8i	−0.0849215	+	0.0849215i
$786$	−283615.	+	283615.i	−0.459075	+	0.459075i
$787$	−108003.	−	108003.i	−0.174376	−	0.174376i	0.614523	−	0.788899i	$-0.289349\pi$
$787$	−108003.	−	108003.i	−0.174376	−	0.174376i	−0.788899	+	0.614523i	$0.789349\pi$
$788$	−116972.	−	116972.i	−0.188377	−	0.188377i
$789$	−493154.			−0.792189
$790$		−	29946.2i		−	0.0479831i
$791$	−508269.	−	508269.i	−0.812345	−	0.812345i
$792$		−	125049.i		−	0.199357i
$793$	34066.6	+	147845.i	0.0541729	+	0.235105i
$794$	−251004.			−0.398144
$795$	403273.	−	403273.i	0.638065	−	0.638065i
$796$	−117529.			−0.185489
$797$		−	196692.i		−	0.309649i	−0.987942	−	0.154824i	$-0.950519\pi$
$797$		−	196692.i		−	0.309649i	0.987942	−	0.154824i	$-0.0494812\pi$
$798$	175361.	−	175361.i	0.275376	−	0.275376i
$799$	577272.	−	577272.i	0.904246	−	0.904246i
$800$	331917.	+	331917.i	0.518620	+	0.518620i
$801$	52610.9	+	52610.9i	0.0819994	+	0.0819994i
$802$	8293.53			0.0128941
$803$			292594.i			0.453768i
$804$	280347.	+	280347.i	0.433694	+	0.433694i
$805$		−	61963.6i		−	0.0956192i
$806$	−419484.	+	96657.6i	−0.645722	+	0.148787i
$807$	482113.			0.740290
$808$	−398626.	+	398626.i	−0.610581	+	0.610581i
$809$	−171772.			−0.262455			−0.131228	−	0.991352i	$-0.541892\pi$
$809$	−171772.			−0.262455			−0.131228	+	0.991352i	$0.541892\pi$
$810$		−	187109.i		−	0.285184i
$811$	−801579.	+	801579.i	−1.21872	+	1.21872i	−0.250642	+	0.968080i	$0.580642\pi$
$811$	−801579.	+	801579.i	−1.21872	+	1.21872i	−0.968080	+	0.250642i	$0.919358\pi$
$812$	848026.	−	848026.i	1.28617	−	1.28617i
$813$	290362.	+	290362.i	0.439297	+	0.439297i
$814$	−81780.8	−	81780.8i	−0.123425	−	0.123425i
$815$	423044.			0.636899
$816$		−	309323.i		−	0.464550i
$817$	−332882.	−	332882.i	−0.498708	−	0.498708i
$818$			120936.i			0.180738i
$819$	−108203.	+	172997.i	−0.161314	+	0.257912i
$820$	−127795.			−0.190058
$821$	−840896.	+	840896.i	−1.24754	+	1.24754i	−0.290742	+	0.956801i	$0.593902\pi$
$821$	−840896.	+	840896.i	−1.24754	+	1.24754i	−0.956801	+	0.290742i	$0.906098\pi$
$822$	−21723.5			−0.0321504
$823$		−	1.00240e6i		−	1.47993i	−0.672646	−	0.739964i	$-0.734842\pi$
$823$		−	1.00240e6i		−	1.47993i	0.672646	−	0.739964i	$-0.265158\pi$
$824$	−493384.	+	493384.i	−0.726659	+	0.726659i
$825$	−408947.	+	408947.i	−0.600841	+	0.600841i
$826$	−186865.	−	186865.i	−0.273885	−	0.273885i
$827$	238471.	+	238471.i	0.348679	+	0.348679i	0.859617	−	0.510939i	$-0.170702\pi$
$827$	238471.	+	238471.i	0.348679	+	0.348679i	−0.510939	+	0.859617i	$0.670702\pi$
$828$	−16823.2			−0.0245384
$829$			188792.i			0.274711i	0.990522	+	0.137355i	$0.0438602\pi$
$829$			188792.i			0.274711i	−0.990522	+	0.137355i	$0.956140\pi$
$830$	−63542.7	−	63542.7i	−0.0922379	−	0.0922379i
$831$		−	1.21795e6i		−	1.76371i
$832$	41864.4	−	9646.40i	0.0604781	−	0.0139354i
$833$	−556716.			−0.802313
$834$	282593.	−	282593.i	0.406283	−	0.406283i
$835$	−215270.			−0.308752
$836$			332213.i			0.475340i
$837$	607895.	−	607895.i	0.867716	−	0.867716i
$838$	−88794.1	+	88794.1i	−0.126443	+	0.126443i
$839$	380475.	+	380475.i	0.540508	+	0.540508i	0.923678	−	0.383170i	$-0.125168\pi$
$839$	380475.	+	380475.i	0.540508	+	0.540508i	−0.383170	+	0.923678i	$0.625168\pi$
$840$	319267.	+	319267.i	0.452476	+	0.452476i
$841$	1.42134e6			2.00958
$842$		−	489780.i		−	0.690839i
$843$	916334.	+	916334.i	1.28943	+	1.28943i
$844$			677384.i			0.950934i
$845$	−122344.	+	354333.i	−0.171344	+	0.496248i
$846$	93354.6			0.130435
$847$	81327.1	−	81327.1i	0.113362	−	0.113362i
$848$	−452312.			−0.628993
$849$		−	192919.i		−	0.267646i
$850$	176652.	−	176652.i	0.244501	−	0.244501i
$851$	−24987.5	+	24987.5i	−0.0345036	+	0.0345036i
$852$	−152918.	−	152918.i	−0.210659	−	0.210659i
$853$	904173.	+	904173.i	1.24266	+	1.24266i	0.958892	+	0.283771i	$0.0915856\pi$
$853$	904173.	+	904173.i	1.24266	+	1.24266i	0.283771	+	0.958892i	$0.408414\pi$
$854$	−108311.			−0.148511
$855$		−	50007.4i		−	0.0684073i
$856$	188545.	+	188545.i	0.257316	+	0.257316i
$857$		−	544039.i		−	0.740744i	−0.928883	−	0.370372i	$-0.879230\pi$
$857$		−	544039.i		−	0.740744i	0.928883	−	0.370372i	$-0.120770\pi$
$858$	89552.2	+	388647.i	0.121647	+	0.527936i
$859$	−265582.			−0.359925			−0.179963	−	0.983673i	$-0.557598\pi$
$859$	−265582.			−0.359925			−0.179963	+	0.983673i	$0.557598\pi$
$860$	266850.	−	266850.i	0.360803	−	0.360803i
$861$	503886.			0.679714
$862$			174644.i			0.235038i
$863$	412705.	−	412705.i	0.554139	−	0.554139i	−0.373494	−	0.927633i	$-0.621840\pi$
$863$	412705.	−	412705.i	0.554139	−	0.554139i	0.927633	+	0.373494i	$0.121840\pi$
$864$	−457121.	+	457121.i	−0.612355	+	0.612355i
$865$	−67434.2	−	67434.2i	−0.0901256	−	0.0901256i
$866$	243493.	+	243493.i	0.324676	+	0.324676i
$867$	−56804.1			−0.0755686
$868$			1.13337e6i			1.50429i
$869$	−111845.	−	111845.i	−0.148107	−	0.148107i
$870$			352855.i			0.466185i
$871$	−452473.	−	283004.i	−0.596426	−	0.373041i
$872$	−464617.			−0.611029
$873$	−77447.1	+	77447.1i	−0.101619	+	0.101619i
$874$	−27523.2			−0.0360309
$875$		−	923764.i		−	1.20655i
$876$	−202819.	+	202819.i	−0.264302	+	0.264302i
$877$	163839.	−	163839.i	0.213018	−	0.213018i	−0.592530	−	0.805548i	$-0.701871\pi$
$877$	163839.	−	163839.i	0.213018	−	0.213018i	0.805548	+	0.592530i	$0.201871\pi$
$878$	139305.	+	139305.i	0.180708	+	0.180708i
$879$	−729548.	−	729548.i	−0.944226	−	0.944226i
$880$	−174523.			−0.225365
$881$		−	852288.i		−	1.09808i	−0.835796	−	0.549041i	$-0.814993\pi$
$881$		−	852288.i		−	1.09808i	0.835796	−	0.549041i	$-0.185007\pi$
$882$	−45015.2	−	45015.2i	−0.0578658	−	0.0578658i
$883$		−	470317.i		−	0.603211i	−0.953433	−	0.301606i	$-0.902477\pi$
$883$		−	470317.i		−	0.603211i	0.953433	−	0.301606i	$-0.0975226\pi$
$884$	142665.	+	619153.i	0.182563	+	0.792307i
$885$	−286753.			−0.366118
$886$	−118477.	+	118477.i	−0.150926	+	0.150926i
$887$	699651.			0.889271			0.444635	−	0.895712i	$-0.353333\pi$
$887$	699651.			0.889271			0.444635	+	0.895712i	$0.353333\pi$
$888$		−	257496.i		−	0.326546i
$889$	770359.	−	770359.i	0.974743	−	0.974743i
$890$	−68999.0	+	68999.0i	−0.0871089	+	0.0871089i
$891$	−698826.	−	698826.i	−0.880265	−	0.880265i
$892$	341930.	+	341930.i	0.429742	+	0.429742i
$893$	−563270.			−0.706340
$894$		−	734335.i		−	0.918797i
$895$	173605.	+	173605.i	0.216729	+	0.216729i
$896$		−	1.05268e6i		−	1.31124i
$897$	118748.	−	27362.0i	0.147585	−	0.0340066i
$898$	−139860.			−0.173437
$899$	−1.42243e6	+	1.42243e6i	−1.75999	+	1.75999i
$900$	−105357.			−0.130071
$901$			1.30123e6i			1.60289i
$902$	129419.	−	129419.i	0.159068	−	0.159068i
$903$	−1.05217e6	+	1.05217e6i	−1.29036	+	1.29036i
$904$	−411033.	−	411033.i	−0.502967	−	0.502967i
$905$	138573.	+	138573.i	0.169193	+	0.169193i
$906$	396780.			0.483385
$907$		−	299763.i		−	0.364387i	−0.983263	−	0.182194i	$-0.941680\pi$
$907$		−	299763.i		−	0.364387i	0.983263	−	0.182194i	$-0.0583198\pi$
$908$	−799164.	−	799164.i	−0.969313	−	0.969313i
$909$		−	197352.i		−	0.238843i
$910$	−226885.	−	141908.i	−0.273983	−	0.171366i
$911$	1.46063e6			1.75996			0.879980	−	0.475010i	$-0.157556\pi$
$911$	1.46063e6			1.75996			0.879980	+	0.475010i	$0.157556\pi$
$912$	−150910.	+	150910.i	−0.181438	+	0.181438i
$913$	−474645.			−0.569413
$914$			55923.5i			0.0669425i
$915$	−83103.9	+	83103.9i	−0.0992611	+	0.0992611i
$916$	−267450.	+	267450.i	−0.318751	+	0.318751i
$917$	−1.00515e6	−	1.00515e6i	−1.19534	−	1.19534i
$918$	243288.	+	243288.i	0.288692	+	0.288692i
$919$	386349.			0.457456			0.228728	−	0.973490i	$-0.426543\pi$
$919$	386349.			0.457456			0.228728	+	0.973490i	$0.426543\pi$
$920$		−	50109.5i		−	0.0592031i
$921$	483638.	+	483638.i	0.570165	+	0.570165i
$922$			588886.i			0.692738i
$923$	246807.	+	154368.i	0.289703	+	0.181198i
$924$	1.05005e6			1.22989
$925$	−156488.	+	156488.i	−0.182893	+	0.182893i
$926$	−4518.51			−0.00526955
$927$		−	244264.i		−	0.284250i
$928$	1.06963e6	−	1.06963e6i	1.24204	−	1.24204i
$929$	−59576.2	+	59576.2i	−0.0690306	+	0.0690306i	−0.740779	−	0.671749i	$-0.765544\pi$
$929$	−59576.2	+	59576.2i	−0.0690306	+	0.0690306i	0.671749	+	0.740779i	$0.265544\pi$
$930$	−235792.	−	235792.i	−0.272623	−	0.272623i
$931$	271607.	+	271607.i	0.313358	+	0.313358i
$932$	93323.7			0.107439
$933$			773681.i			0.888789i
$934$	172323.	+	172323.i	0.197537	+	0.197537i
$935$			502074.i			0.574308i
$936$	−87502.9	+	139902.i	−0.0998782	+	0.159687i
$937$	507904.			0.578499			0.289250	−	0.957254i	$-0.406594\pi$
$937$	507904.			0.578499			0.289250	+	0.957254i	$0.406594\pi$
$938$	269404.	−	269404.i	0.306196	−	0.306196i
$939$	−1.53848e6			−1.74486
$940$		−	451537.i		−	0.511019i
$941$	−494292.	+	494292.i	−0.558219	+	0.558219i	−0.928800	−	0.370581i	$-0.879159\pi$
$941$	−494292.	+	494292.i	−0.558219	+	0.558219i	0.370581	+	0.928800i	$0.379159\pi$
$942$	73470.6	−	73470.6i	0.0827964	−	0.0827964i
$943$	−39542.9	−	39542.9i	−0.0444677	−	0.0444677i
$944$	160811.	+	160811.i	0.180456	+	0.180456i
$945$	534436.			0.598456
$946$			540480.i			0.603945i
$947$	−472638.	−	472638.i	−0.527022	−	0.527022i	0.392661	−	0.919683i	$-0.371555\pi$
$947$	−472638.	−	472638.i	−0.527022	−	0.527022i	−0.919683	+	0.392661i	$0.871555\pi$
$948$		−	155056.i		−	0.172533i
$949$	204742.	−	327345.i	0.227339	−	0.363474i
$950$	−172368.			−0.190989
$951$	813757.	−	813757.i	0.899775	−	0.899775i
$952$	−1.03017e6			−1.13667
$953$		−	926281.i		−	1.01990i	−0.860204	−	0.509949i	$-0.829664\pi$
$953$		−	926281.i		−	1.01990i	0.860204	−	0.509949i	$-0.170336\pi$
$954$	−105215.	+	105215.i	−0.115607	+	0.115607i
$955$	−318306.	+	318306.i	−0.349010	+	0.349010i
$956$	508600.	+	508600.i	0.556494	+	0.556494i
$957$	1.31786e6	+	1.31786e6i	1.43895	+	1.43895i
$958$	−297422.			−0.324072
$959$		−	76989.2i		−	0.0837129i
$960$	23532.0	+	23532.0i	0.0255338	+	0.0255338i
$961$		−	977522.i		−	1.05847i
$962$	34268.1	+	148720.i	0.0370288	+	0.160701i
$963$	−93344.8			−0.100656
$964$	828903.	−	828903.i	0.891969	−	0.891969i
$965$	−93614.4			−0.100528
$966$			86994.8i			0.0932264i
$967$	−123341.	+	123341.i	−0.131903	+	0.131903i	−0.769976	−	0.638073i	$-0.779732\pi$
$967$	−123341.	+	123341.i	−0.131903	+	0.131903i	0.638073	+	0.769976i	$0.279732\pi$
$968$	65768.6	−	65768.6i	0.0701888	−	0.0701888i
$969$	434146.	+	434146.i	0.462368	+	0.462368i
$970$	−101572.	−	101572.i	−0.107952	−	0.107952i
$971$	134660.			0.142824			0.0714120	−	0.997447i	$-0.477249\pi$
$971$	134660.			0.142824			0.0714120	+	0.997447i	$0.477249\pi$
$972$		−	333113.i		−	0.352581i
$973$	1.00152e6	+	1.00152e6i	1.05788	+	1.05788i
$974$		−	659480.i		−	0.695158i
$975$	743678.	−	171359.i	0.782305	−	0.180259i
$976$	93209.4			0.0978498
$977$	−1.21699e6	+	1.21699e6i	−1.27497	+	1.27497i	−0.331518	+	0.943449i	$0.607561\pi$
$977$	−1.21699e6	+	1.21699e6i	−1.27497	+	1.27497i	−0.943449	+	0.331518i	$0.892439\pi$
$978$	−593939.			−0.620961
$979$			515402.i			0.537750i
$980$	−217729.	+	217729.i	−0.226707	+	0.226707i
$981$	115011.	−	115011.i	0.119509	−	0.119509i
$982$	439794.	+	439794.i	0.456064	+	0.456064i
$983$	−330188.	−	330188.i	−0.341708	−	0.341708i	0.515301	−	0.857009i	$-0.327680\pi$
$983$	−330188.	−	330188.i	−0.341708	−	0.341708i	−0.857009	+	0.515301i	$0.827680\pi$
$984$	407489.			0.420848
$985$			172492.i			0.177785i
$986$	−569274.	−	569274.i	−0.585555	−	0.585555i
$987$			1.78038e6i			1.82759i
$988$	232465.	−	371670.i	0.238147	−	0.380754i
$989$	165140.			0.168834
$990$	−40596.9	+	40596.9i	−0.0414212	+	0.0414212i
$991$	131994.			0.134402			0.0672010	−	0.997739i	$-0.478593\pi$
$991$	131994.			0.134402			0.0672010	+	0.997739i	$0.478593\pi$
$992$			1.42953e6i			1.45268i
$993$	1.17343e6	−	1.17343e6i	1.19003	−	1.19003i
$994$	−146950.	+	146950.i	−0.148729	+	0.148729i
$995$	86656.8	+	86656.8i	0.0875299	+	0.0875299i
$996$	−329012.	−	329012.i	−0.331660	−	0.331660i
$997$	−981116.			−0.987029			−0.493514	−	0.869738i	$-0.664288\pi$
$997$	−981116.			−0.987029			−0.493514	+	0.869738i	$0.664288\pi$
$998$			624554.i			0.627060i
$999$	−215517.	−	215517.i	−0.215949	−	0.215949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.5.d.a.5.2	✓	6
3.2	odd	2		117.5.j.a.109.2		6
4.3	odd	2		208.5.t.c.161.1		6
13.5	odd	4		169.5.d.a.99.2		6
13.8	odd	4	inner	13.5.d.a.8.2	yes	6
13.12	even	2		169.5.d.a.70.2		6
39.8	even	4		117.5.j.a.73.2		6
52.47	even	4		208.5.t.c.177.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.d.a.5.2	✓	6	1.1	even	1	trivial
13.5.d.a.8.2	yes	6	13.8	odd	4	inner
117.5.j.a.73.2		6	39.8	even	4
117.5.j.a.109.2		6	3.2	odd	2
169.5.d.a.70.2		6	13.12	even	2
169.5.d.a.99.2		6	13.5	odd	4
208.5.t.c.161.1		6	4.3	odd	2
208.5.t.c.177.1		6	52.47	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30633 + 1.30633i) q^{2} +9.97438 q^{3} +12.5870i q^{4} +(9.28070 - 9.28070i) q^{5} +(-13.0298 + 13.0298i) q^{6} +(-46.1782 - 46.1782i) q^{7} +(-37.3440 - 37.3440i) q^{8} +18.4882 q^{9} +O(q^{10})\)	\(q+(-1.30633 + 1.30633i) q^{2} +9.97438 q^{3} +12.5870i q^{4} +(9.28070 - 9.28070i) q^{5} +(-13.0298 + 13.0298i) q^{6} +(-46.1782 - 46.1782i) q^{7} +(-37.3440 - 37.3440i) q^{8} +18.4882 q^{9} +24.2472i q^{10} +(90.5598 + 90.5598i) q^{11} +125.548i q^{12} +(-37.9467 - 164.685i) q^{13} +120.648 q^{14} +(92.5693 - 92.5693i) q^{15} -103.826 q^{16} +298.690i q^{17} +(-24.1516 + 24.1516i) q^{18} +(145.723 - 145.723i) q^{19} +(116.816 + 116.816i) q^{20} +(-460.599 - 460.599i) q^{21} -236.601 q^{22} +72.2918i q^{23} +(-372.483 - 372.483i) q^{24} +452.737i q^{25} +(264.702 + 165.561i) q^{26} -623.516 q^{27} +(581.247 - 581.247i) q^{28} +1458.98 q^{29} +241.851i q^{30} +(-974.947 + 974.947i) q^{31} +(733.134 - 733.134i) q^{32} +(903.278 + 903.278i) q^{33} +(-390.187 - 390.187i) q^{34} -857.133 q^{35} +232.712i q^{36} +(345.648 + 345.648i) q^{37} +380.723i q^{38} +(-378.495 - 1642.63i) q^{39} -693.156 q^{40} +(-546.990 + 546.990i) q^{41} +1203.38 q^{42} -2284.35i q^{43} +(-1139.88 + 1139.88i) q^{44} +(171.584 - 171.584i) q^{45} +(-94.4365 - 94.4365i) q^{46} +(-1932.68 - 1932.68i) q^{47} -1035.60 q^{48} +1863.86i q^{49} +(-591.422 - 591.422i) q^{50} +2979.25i q^{51} +(2072.89 - 477.636i) q^{52} +4356.45 q^{53} +(814.515 - 814.515i) q^{54} +1680.92 q^{55} +3448.95i q^{56} +(1453.50 - 1453.50i) q^{57} +(-1905.90 + 1905.90i) q^{58} +(-1548.85 - 1548.85i) q^{59} +(1165.17 + 1165.17i) q^{60} -897.748 q^{61} -2547.20i q^{62} +(-853.754 - 853.754i) q^{63} +254.209i q^{64} +(-1880.56 - 1176.22i) q^{65} -2359.95 q^{66} +(2232.99 - 2232.99i) q^{67} -3759.63 q^{68} +721.065i q^{69} +(1119.69 - 1119.69i) q^{70} +(-1218.01 + 1218.01i) q^{71} +(-690.424 - 690.424i) q^{72} +(1615.47 + 1615.47i) q^{73} -903.058 q^{74} +4515.77i q^{75} +(1834.22 + 1834.22i) q^{76} -8363.78i q^{77} +(2640.24 + 1651.37i) q^{78} -1235.04 q^{79} +(-963.576 + 963.576i) q^{80} -7716.73 q^{81} -1429.09i q^{82} +(-2620.61 + 2620.61i) q^{83} +(5797.57 - 5797.57i) q^{84} +(2772.06 + 2772.06i) q^{85} +(2984.10 + 2984.10i) q^{86} +14552.4 q^{87} -6763.72i q^{88} +(2845.64 + 2845.64i) q^{89} +448.288i q^{90} +(-5852.54 + 9357.16i) q^{91} -909.938 q^{92} +(-9724.49 + 9724.49i) q^{93} +5049.40 q^{94} -2704.82i q^{95} +(7312.55 - 7312.55i) q^{96} +(-4189.00 + 4189.00i) q^{97} +(-2434.80 - 2434.80i) q^{98} +(1674.29 + 1674.29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9} - 32 q^{11} - 244 q^{14} + 404 q^{15} + 1044 q^{16} - 802 q^{18} + 732 q^{19} + 428 q^{20} - 2128 q^{21} - 1632 q^{22} - 24 q^{24} + 910 q^{26} + 236 q^{27} + 1884 q^{28} + 4184 q^{29} - 3468 q^{31} + 2092 q^{32} + 2324 q^{33} - 5304 q^{34} - 4204 q^{35} - 1758 q^{37} + 1196 q^{39} - 708 q^{40} + 4750 q^{41} + 9532 q^{42} - 3956 q^{44} + 830 q^{45} + 516 q^{46} - 6872 q^{47} - 9436 q^{48} - 322 q^{50} + 3900 q^{52} + 2108 q^{53} - 184 q^{54} + 6408 q^{55} - 5800 q^{57} + 6516 q^{58} + 4372 q^{59} + 1324 q^{60} + 5988 q^{61} - 652 q^{63} - 5018 q^{65} - 4592 q^{66} + 72 q^{67} - 10572 q^{68} + 7368 q^{70} - 14672 q^{71} - 7980 q^{72} + 5874 q^{73} + 1544 q^{74} + 3576 q^{76} + 5720 q^{78} + 2616 q^{79} - 12080 q^{80} - 19450 q^{81} + 19264 q^{83} + 6296 q^{84} + 4164 q^{85} + 29376 q^{86} + 35584 q^{87} - 986 q^{89} - 30888 q^{91} + 5304 q^{92} - 9520 q^{93} - 36156 q^{94} + 20720 q^{96} - 23154 q^{97} - 41426 q^{98} + 17492 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9 - 32 * q^11 - 244 * q^14 + 404 * q^15 + 1044 * q^16 - 802 * q^18 + 732 * q^19 + 428 * q^20 - 2128 * q^21 - 1632 * q^22 - 24 * q^24 + 910 * q^26 + 236 * q^27 + 1884 * q^28 + 4184 * q^29 - 3468 * q^31 + 2092 * q^32 + 2324 * q^33 - 5304 * q^34 - 4204 * q^35 - 1758 * q^37 + 1196 * q^39 - 708 * q^40 + 4750 * q^41 + 9532 * q^42 - 3956 * q^44 + 830 * q^45 + 516 * q^46 - 6872 * q^47 - 9436 * q^48 - 322 * q^50 + 3900 * q^52 + 2108 * q^53 - 184 * q^54 + 6408 * q^55 - 5800 * q^57 + 6516 * q^58 + 4372 * q^59 + 1324 * q^60 + 5988 * q^61 - 652 * q^63 - 5018 * q^65 - 4592 * q^66 + 72 * q^67 - 10572 * q^68 + 7368 * q^70 - 14672 * q^71 - 7980 * q^72 + 5874 * q^73 + 1544 * q^74 + 3576 * q^76 + 5720 * q^78 + 2616 * q^79 - 12080 * q^80 - 19450 * q^81 + 19264 * q^83 + 6296 * q^84 + 4164 * q^85 + 29376 * q^86 + 35584 * q^87 - 986 * q^89 - 30888 * q^91 + 5304 * q^92 - 9520 * q^93 - 36156 * q^94 + 20720 * q^96 - 23154 * q^97 - 41426 * q^98 + 17492 * q^99

Introduction

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